If Iraq showed one thing, it's that a full scale Chinese - U.S. war would be a nightmare and something that I think is already not possible to win by either side, but if I had to bet on one side, then perhaps the Chinese - they are more likely to have the manpower, eventually and theoretically, to occupy the U.S. than vice versa.
If anything would go down, it would probably be a war over Taiwan, that would leave Taiwan in ruins and would end with one of the two parties conceding defeat over the island. For now I consider it more likely though that China is looking to scare Taiwan into coming back under Chinese influence, in a manner like Hong Kong did. They're making a good show already of supporting the political party that supports the Chinese Republic, and its also a good way to prevent the U.S. from meddling - if Taiwan democratically chooses to return to China, they have little grounds on which they can 'defend' Taiwan from Chinese influence.
In a sense, also, the U.S.'s recent aggressive stance scares China into becoming a military superpower. And it makes sense. Although I'm not necessarily looking forward to it, there is definitely room for another military superpower on this planet. Hopefully we've come past the point though where they consider it a realistic option to compete over world-domination.
