Not China; not the United States. The gold medal for interstate warfare was snatched up by Russia, and that one is worth more than all the others combined! Poor China; it spent $100 million on the opening ceremony alone and walked away with just a bunch of medallions; for a lot less, Russia got a chunk of territory and a formidable reputation not to be messed with.
I agree with Ilya that Russia is not a threat to the United States in the way that the Soviet Union was; my interest is in what the conquest of South Ossetia tells us about international law. Here, Ilya's concern about soft power comes into play. But soft power cuts in multiple ways.
If you're the dictator or even duly elected president of some small state somewhere, with gas reserves or space for a military base or some such thing, who would you rather deal with? Russia or China, who will make a deal with you and then leave you alone, or the United States or Europe, which will make a deal with you, and then start bleating about your human rights record, or the fairness of your elections, or the integrity of your judges, or your devotion to the rule of law, or your persecution of religious minorities, or your treatment of women -- which looks so fine to us, but looks like neocolonialism to them. Inward-looking nationalistic states, with nothing to offer in terms of a universal ideology, have a tactical advantage, it seems to me; and we will see more of this as Russia and China begin to flex their muscles.
Of course, nationalistic regimes have a tendency to self-destruct -- "we are better than the rest of the world" can't be true for more than one state at a time. Russia's neighbors are terrified of it, and so some like Poland are being driven even more deeply into the arms of the west. But the danger that the United States will find itself being manipulated to advance the local ambitions of those states — which is essentially what Georgia tried to do — is significant, and we should recognize what the Russians did to Georgia in our own Monroe Doctrine (which since 1989 has been extended from the western hemisphere to more or less everywhere). In the long term, the United States and Europe are less of a threat to states that actually give in and adopt western norms than Russia and China are, if the democratic peace literature (which says that democracies do not fight with each other) is to be believed, and that is, I suppose, what our soft power amounts to. But the long term just never seems to arrive, does it?