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The US would never fight a conventional war with China or Russia, but might support a country that did (as with Afghanistan from 1979 to 1989). Russia has a much larger conventional army, and China an even larger one. Any armed conflict would likely lead to a nuclear exchange, either limited or total. Russia has parity with the US in nuclear weapons, while China is still a distant 3rd.
It would be 50/50 depending on if allies are allowed or not. If no allies then America would probably just win due to superior technology. If Russia performed a surprise attack they would win due to having a quite good military and would leave America little time to react by which time they would be destroyed. If allies were allowed America would win easily due to close ties with the UK as the UK has about the second best military in the world (after America) so that's the best and the second best together making a formidable force and that's not counting the EU who would help the UK, Russia would get China but lets face it all they have is loads of unskilled people and poor technology (they are a backward country in many ways). To sum up America would come out on top in most situations. If nukes are involved we are all going to die.
The elephant would win.
obviously army to army Persians would win by tactics but one to one a barbarian would win
raiden would win