So, bear with me a second and try not to just reflexively shout Murica! as the answer to any question regarding US vs the rest of the world.
Looking strictly at the federal government and not at the lower levels as there is not a good way to compare regions, and taking the definition of corruption as any form of bribery or malfeasance even if technically "legal" I think we may actually lose in that comparison. My thought process.
Russia is a corrupt oligarchy, where a couple dozen men have become billionaires because of sweetheart (illegal) deals. Compared to America, there are far more blatant and egregious violations of laws. But actually look at the American system for a second. Insider trading laws don't apply to Congress, so they can make millions and millions of dollars buying/selling/shorting stocks based on advance knowledge of their own laws/regulations etc. Completely legal. They can funnel billions to contractors, then leave office and get seven figure sinecure jobs with those contractors. Completely legal. Hell, the ability to syphon off millions or billions in tax dollars for your constituents in pork is a well known measure of how "effective" a politician is, and is in no significant way different than Putin skimming billions for his buddies.
Is scamming hundreds of millions or billions of dollars for your "associates" to build a ridiculous (car/solar project/pointless bridge etc etc) really any different than scamming money for your friends who don't bother to go through the pretense? Is making a few dozen billionaires better or worse than making many thousands of millionaires with wasted tax dollars? What's the difference between "Give me $10 million and I'll send you $100 million" and "I'll give you $100 million to 'research' this 'new tech' wink wink nudge nudge if you'll give me a $10 million salary at your company after I leave office"? Sure one is technically legal and one isn't, but are they actually different in any real sense of the word?
As far as I can tell, the main difference between the US and RU fed.govs is that one pretends there is no corruption and the other just went ahead and legalized it.