1. His infantry are better than yours.
His basic soldier is the initiate. It costs the same as a GI and does double the damage. If they hunker down in a building (say, the one chokepoint approaching your base), their damage per second is retarded. They mop up tanks in about half a second.
Instead of attack dogs he has Brutes. They can't sniff out spies (not that you'll see many of those), but they can punch tanks. They're basically grey The Hulks (not to be confused with Doomsday or Grey The Hulk). They can't be run over. They cost half the price of a tank.
For $700 he can make a sniper. The only other sniper in RA2 is the British Sniper, which costs $1000. Whenever this sniper (the Virus) kills a soldier, it leaves an AOE pool of gas that kills more soldiers if they run through it.
His only other infantry are Yuri clones and Yuri Himself. Well, that and engineers which are the same as any engineers.
2. His buildings are better than yours.
His power plant costs $600, the same as the Soviet Tesla Reactor. It gives the same power. However, you can place infantry inside and get gigantic boosts to power. While other players have to work in additional power while they're pumping out the refineries and war factories, he just makes one then sticks a bunch of infantry inside.
His radar dish tells him when you've started to make a move on his base.
His static defense structure is a pair of gigantic Gatling guns. They work on everything. The longer they shoot, the higher their damage per second.
His refinery is a unit. You can build it from War Factories or from the con yard. It consumes no power since it's a unit. It moves over to the ore, digs in and sends out infinitely respawning slaves to gather the ore. A full shipment from each slave has higher yield than Allied or Soviet miners. The slaves also walk like two metres back to the refinery instead of driving half a kilometer. Thus, he has the most efficient way of gaining finances.
He can build a cloning vat. It gives you a free infantry for every infantry you make. That means if he bothers to go to late game tech, he can get free Brutes. Or free Yuri Clones.
He also has the Grinder instead of a repair depot. I'll talk about that in the next section.
Superweapons aren't used very often in multiplayer due to the tank-based meta, but his are also better than yours. The Genetic Mutator turns any infantry in its reach into Brutes that work for him. These can wreak havoc on someone trying to make soldiers to stop your regular Brutes backing up your tank platoon. Or you could just use this on some slaves in an area without much ore and get free brutes. His other superweapon is the Psychic Dominator. It sets off a big-ass explosion like the nuclear missile, but also mind controls everything in the center of the blast. Sure hope you didn't have your tanks bunched up ever.
3. His navy only has two units. They're better than all of yours.
He has a hovercraft transport like the other two factions. At mid tech he gains the Boomer Submarine. It's $2000, the price of a capital ship. It does double the damage of the Soviet submarine. It has slightly less reach than the Soviet Dreadnought, but does more damage. It's available a full tech level before the other navies are allowed to start going.
4. Mind Control
The Soviet hero infantry unit in Vanilla was the Yuri Clone. A clone of Yuri that could control the mind of a single unit, but lost that control if they died or chose a different target. They cost $1200 each and were a late tech unit. Yuri's Yuri Clones cost $600. They are a mid tech unit.
Mind control wreaks havoc on tank platoons. For a unit that costs less than a tank he can mess with your platoon if you aren't micromanaging it. He can whittle down your forces with little risk to himself. He can also shove mind controlled infantry into his power plants (which frees up the Yuri Clone to steal something else). On top of that, he has a building called The Grinder. Any unit placed in the Grinder is, well, ground up and turned into money. He can turn your money into his own.
He also has a static defense structure version that can hold 3 units. He also has a mind controlling tank called the Mastermind. These are both good, but nowhere near as cost effective as the basic clones.
Did I mention that mind control units can all detect spies? Good luck trying to steal that money back.
5. The Flying Disc Exists
If he's toying with you and progressing to late game, he gains the Flying Disc. It's a flying disc that shoots lasers of reasonable damage. If you place it over a building, it does things. If you place it over a static defense structure, it shuts the thing down. If you place the disc over a refinery, it starts stealing the money and sending it directly to you. If you place it over any power station, it shuts down that player's power. That means slower production, a halt on superweapon charge times and no minimap access.
6. He completely destroys C&C Meta in a whole other way.
This is the big one. This is the number one reason he destroys the game. Remember how I said C&C is all about efficiently pumping out tanks because they do everything? He has a way to stop this beyond brutes. Say hell to the Magnetron.
Need a little force?
The magnetron was intended to be Yuri's siege unit. It shoots magnetic blasts at buildings that damage them. It also picks up tanks and drags them towards himself to be mind controlled or pelted with gatling fire on the way since they're classed as airborne. Irritating, but possible to deal with, right?
Suppose a magnetron starts to lift up a tank, then switches target. As soon as the magnet beam hits, the tank has to go through the whole levitation animation, then the falling animation. It cannot do anything in this time. Suppose a magnetron keeps switching targets across the whole platoon. It means your 50 tanks are juggled up and down over and over while his tanks zip past and blow up your base. This technique was known as mag-juggling. More than anything else this got his faction banned in online play. Yuri had complete control of any territory, all with a single mid-tech unit that only cost $100 more than a Soviet tank. It was incredibly stupid.
So that's the rundown. I probably forgot other things along the way, but as you can see you could run with pretty much whatever build you wanted so long as you had a magnetron keeping you safe. Yuri was the zenith of Westwood's creativity with units, and for once they managed to make options so powerful that there were reasons to make them over the basic tank.