Each faction's Anti-Air weapon systems are tailored perfectly to counter whichever method of air attacks the opposing faction prefers:
The Allies use slow-firing, powerful missiles. The Soviets' only relevant air unit is the slow, heavily-armored Kirov Airship, as the Siege Chopper is mostly used in its grounded mode, the MiGs require Boris target-painting ability. The V3 Rocket Launcher fires rockets slower than Patriot Missile systems fire, so they have it covered as well. The Spy Plane support power is the only air unit the Allies have no specific defense against. Guardian GIs and IFVs show this trait well as they are used as anti-ground armor despite having an equally-strong anti-air attack.
The Soviets use fairly fast-firing flak guns that deal Splash Damage. The Allies have a significantly higher amount of air units, but most of them fall into the same category: Fragile Speedsters. Flak Cannons, Flak Tracks, Flack Troopers and Sea Scorpions can damage several air units at the same time with their attacks, forcing the Allies to bring support to take those anti-air defenses down or Zerg Rush to overwhelm them.
Yuri's faction goes Gatling Good with Gatling Cannons and Gatling Tanks. They are much better against frail air units than against heavily-armored ones as they rev up to max speed to have a chance to take them down (whereas Yuri doesn't have such a problem against ground armor thanks to Psychic Towers). This fits perfectly to counter Allied air strikes but not against Soviet Kirov assaults, and when you consider the Allies won the war in the vanilla game...
Why are the enemy attacks far more relentless in the mission "Deja Vu" despite this essentially being the same mission as "Mirage", where the enemy assaults were scripted and easy to counternote The real reason is due to the AI in the mission not being programmed correctly and will only attack during said scripted encounters.? Because in "Deja Vu", you're essentially fighting a version of yourself, who likely would have steamrolled the Soviet army in the original timeline. Did you expect a fight with the Allied Player Character to be easy?
This also handily explains why the Allies immediately surrender after this mission. Not only did they lose the Chronosphere and the brilliant mind of Albert Einstein, but also their most skilled battlefield commander, all of which were instrumental in winning the war.
It likewise explains why the enemy seemed easier to beat in "Mirage" despite outnumbering the Allies. In all likelihood, the bulk of the USSR's troops at the European front were more fit for garrison duty or holding the line than launching offensives, with many of the best ones set aside for the invasion of the United States. This would also explain why the Soviet Player Character and Zofia seemed absent in the canonical version of events, as they would have still been in North America when Moscow had fallen to Allied hands, just far enough away from the main thrust to escape being captured like Romanov.
In the Allied campaign in Yuri's Revenge, after you go back in time, the war against the Soviet Union is won without you doing a single mission against them. At first, it seemed odd, until upon realizing - your earlier self was still around. The Allies found themselves with two commanders, so they sent one against Yuri, the other against the Soviets. Incidentally, this also means that there are two Tanyas and two Evas.
And there is the tech you bring back that was still being developed at the start of the war, which would have likely given the Allied war effort just enough leeway and advance warning to make victory even more of a certainty.
It can seem odd how Yuri could manage to deploy his forces openly so early in the war without someone like Vladimir or Romanov catching on. Just as on Alcatraz Island in the first mission (and the original RA2's Soviet campaign), it's likely that on top of embedding his men with the invading armies, he mind-controlled or otherwise eliminated anyone who could have sounded the alarm, ensuring that the higher-ups in Moscow were none the wiser until the Allies hand them the truth upon winning the war.
This coincidentally also explains why the hunt for Yuri is so different in the Soviet campaign. With the war ending and Yuri having been exposed much earlier, he simply doesn't have enough time for many of his original plans to even get off the ground compared to the Allied version of events (which has the war playing out more or less on schedule). He's thus left only with even fewer Psychic Dominators on hand (like in London) and is forced to make do with backup schemes (such as the Moon base) before falling back to his Transylvanian hideout, as those are all he has left.
The fact that there are two commanders also provides an in-universe explanation as to why every post-time travel mission (except for Deja Vu) is against Yuri and not the opposing faction - your other self is cleaning up the enemy faction, while you, whom has personally seen the horrors that Yuri unleashed and is the most appropriate for dealing with him, deals with Yuri. The experience angle also explains why you are sent to destroy the Allied Chronosphere in Deja Vu, as since the player would have learnt the details of the Black Forest Chronosphere (given the fact that they provide documents of such to Romanov), they would be the best suited to lead the attack on it.
Yuri's forces tend to be overpowered and often made of pure Nightmare Fuel. Why? Well, why wouldn't a man who is keenly aware of the benefits of breaking an enemy's morale use units that are designed to shock and horrify an enemy soldier? His buddy just exploded into a cloud of toxic gas. His commander is telling him to surrender in a Creepy Monotone. There's a brain on wheels coming over the hill, and a frigging flying saucer overhead. And then his squad gets transformed into grey muscular brutes against their will before going on a rampage. Yuri's not just a good strategist; he's trying to invoke the benefits of Nightmare Fuel.
Given Yuri's background, it also makes sense that his naval doctrine would mirror Stalin's, relying exclusively on Boomer submarines. With his army's focus on both global conquest and weaponizing Nightmare Fuel, having anything more than a means for enacting highly-mobile and undetectable ballistic strikes which could strike fear in the hearts of his enemies would be pointless. It similarly explains how he has ready access to Boomers at all, as they would have likely been updated versions of Red Alert 1's Soviet missile subs, which would have been sidelined amidst Romanov's military reforms.
Yuri's forces, paradoxically, seem comparatively inept when it comes to their Propaganda Machine in contrast to the Brotherhood of Nod (which they're a Corrupted Character Copy of), given the best they could come up with are brainwashing messages from Yuri himself and a half-baked dinosaur movie. While the Psychic Dominator in itself renders propaganda superfluous, it still makes sense for him to control the masses through subliminal messaging, especially when it comes to individuals who may not be as susceptible to overt psionic control. Thus, it doesn't really matter what the actual content is, so long as it serves as a convenient medium to reinforce that control.
As heavy on weaponized Nightmare Fuel as Yuri's forces are, the more "conventional" parts of their arsenal, like their Lasher Tanks, Gatling weapons and Boomer subs, can seem painfully mundane by comparison. Whether they're experimental designs rejected by the USSR as they were rebuilding their military prior to the war or Soviet hand-me-downs relegated to backline duty, Yuri isn't too picky with what he can get his hands on if it means his plans for world conquest can proceed as soon as possible. This would also explain why even Premier Romanov seems more familiar with them than the Allies, as he might have seen some of them in action beforehand.
It's a minor gripe for some Red Alert 2 players that Soviet conscripts are armed with PPSh-41s even though they had access to AK-47s in the last war, and as seen with Boris in Yuri's Revenge, still have the means to make them. However, given that the nation was disarmed following its defeat in that war, it makes sense for something as outdated as the PPSh-41 to be the only small arms they have left in abundance. The Allies might have considered it to be more of a police weapon due to its inferior range and small calibers, and thus allowed the new Soviet regime to keep all of it. Also, nobody expects the Soviets to use a 30-year-old SMG as the new standard issue in the event of another war, so they can mass-produce it without anybody batting an eye.
This can also explain why the Soviets still have access to aircraft other than Kirov Airships, such as the MiG strike fighters and Siege Choppers seen in Yuri's Revenge, albeit used sparingly. Despite the disarmament treaties, it's likely that the Allies might have allowed the USSR to retain a vestigial air force under the logic that it'd be just sufficient to defend the Motherland. Unfortunately for them, this leaves just enough in the way of loopholes for the Soviets to exploit.
While Romanov's established as having an eye for spaceflight in Yuri's Revenge, it can seem rather convenient for the Soviets to have an arsenal modified for Lunar warfare on hand, let alone have military training for such an occasion. Yuri's schemes aside, it's likely that the Premier's prior détente with the Allies gave the USSR enough wiggle room to pursue its own "peaceful" space program without too much oversight. Not to mention those aforementioned loopholes, as nothing was ever really said about banning militarization off-world or barring cosmonauts from being armed with lasers.
In Red Alert 2, the Allies canonically win the war by deploying a strike force straight at the heart of the USSR with a Chronosphere as a Hail Mary gamble. In the Soviet campaign, however, the Allies don't seem to attempt this, with the closest being a desperate raid at the Urals. That is, until one remembers that the reason why the Chronosphere plan works at all is because the Florida Keys was the closest place in America (albeit right next to Communist Cuba) where it could be properly set up to strike at Moscow. Without a successful invasion, itself made possible by much of the US being liberated, the Soviets would have had a better chance of actually winning the conflict.
Moreover, in the Soviet campaign, with the Florida Keys firmly out of reach, the Allies are forced to make do with an alternative near the dwindling territories still under their control, namely Point Hope, Alaska. Despite being a much more desperate measure with less chances of success, however, the Soviets don't know that. Nonetheless, they know enough that it's still too much of a risk to ignore.
In Yuri's Revenge, even with Einstein's genius and having Chronosphere data to work with, to devise a veritable time machine capable of sending back a small army in such short notice seems awfully convenient. Until one remembers the Philadelphia Experiment in Red Alert 1, which he personally oversaw. It's likely that he found the means for safe time travel (rather than simply teleporting through or erasing targets) over the course of his research but purposefully kept the real findings to himself for fear of what might happen if it were to fall in the wrong hands. The imminent threat posed by Yuri, however, forces him to make use of that knowledge, as things couldn't possibly get any worse.
Despite Vladimir being at the forefront of the invasion in the base game, it can seem odd how he's not mentioned at all in the Soviet campaign of Yuri's Revenge. Chances are, his antics over the course of the canonical Allied campaign were among the intel sent by Zofia to Premier Romanov's past self, which would make him disappointed enough to sideline the general for being too incompetent. This would, coincidentally, further bolster the time-travelling commander's credibility in the Premier's eyes for bringing such blunders to his attention early on.
This may also explain why Premier Romanov tries to be more amicable towards the Allied leadership and generally promotes benevolent Communist hegemony in the altered timeline. He would have likely come across Vladimir's nuking of Chicago out of spite (which galvanized the European members of the Allies instead) among the files sent by his future self. Regardless of whether he'd be appalled by it or not, chances are this event might make him realize that simply defeating Yuri alone wouldn't be enough to ensure Soviet victory in the long run.
Why do the Soviets use Flak Tracks, which are half-tracks using a design that dates back to the Second World War and only then? Because the main advantages of half-tracks play perfectly into Soviet doctrine! The main advantages of a half-track is that it combines the versatility, simplicity and cheapness of a wheeled vehicle with the all-terrain ability of a tracked vehicle, while also being easier to train drivers in than full-tracked vehicles, while the strength of the tracks also allowed the half-track to carry powerful weapons such as anti-tank guns and flak cannons. If you're a nation that uses a quantity over quality doctrine like say, the Soviet Union, half-tracks are a cheap and easy weapon that doesn't require any training, so it perfectly fits its doctrine.
In the final Allied Mission, Chrono Storm, it's possible to train Yuri Prime if you go through the convoluted method of infiltrating a spy into the Soviet Battle Lab, then capturing a Soviet Barracks to train him. This is Yuri Prime's sole appearance in either of the campaigns; he doesn't show up in the mission centered around him in the Soviet Campaign. Yuri is taking to the field to prove his usefulness to the Allies, as the Soviet Union is about to be destroyed. This is likely why Yuri's plan in Yuri's Revenge catches everyone off-guard; having just helped them in the final battle, Yuri was likely granted some kind of amnesty in the Allied version of events allowing him to continue to work on the Psychic Dominators in secret.
Given how the introduction to Yuri's Revenge has him being listed as an unaccounted-for war criminal, it's also likely that he may have covertly disguised himself as a turncoat elite operative using Yuri Prime as a codename before disappearing amidst the victory laps, allowing him to gather intel on the Allies for his eventual world domination scheme.
The Arizona monument being present at Pearl Harbor suggests that some version of the Pacific Warstill happened (with all that implies), if not a more powerful Imperial Japan as an unintended result of Einstein's meddling with time. While not quite to the same degree as the Empire of the Rising Sun, this would not only explain why the United States didn't fully join the war against the USSR until the final stages in Red Alert 1, but also why the US has (or had thanks to Yuri) a sizable stockpile of nukes despite the Soviet threat ostensibly not being factor.
This is reinforced by how President Dugan has a Hotline to both Moscow and Tokyo. While Moscow makes sense given the power the Soviets still possess despite being seemingly de-fanged, Tokyo is rather odd. Unless the Japanese are in a similar situation to the Soviets at the time and the Red Alert version of the Pacific War had managed to drag long enough for the US to consider them a threat.
This might also factor into why South Korea is part of the Allies while Japan isn't. Namely as a means for the Americans to keep the defeated Japanese under control in Asia while dealing with the Soviets.
Speaking of South Korea, it seems that despite changes to the timeline after Einstein erased Hitler from existence, the Korean Warstill happened with both halves of Korea still divided. In real life, Korea is divided into North under the Soviets and South under the US after the end of World War II. In Red Alert 1, the Soviets invaded Asia under Radik Gradenko as one of Soviet Union's campaigns of world domination before they ultimately lost in the altered timeline's Second World War with Stalin killed by Nikos Stavros and Romanov being installed as the leader of an Allied puppet regime. There are terrible implications of how Korea still ends up halved into North and South in the Red Alert universe.