The US would win.... IF they were not fighting Iraq and Mexico (Drug War). If they were still in Iraq/Mexico, China would win hans down.
China can't nuke us. Their missiles aren't intercontinental yet, they are just using borrowed Russian missles. This is Russias way of saying increasing its power by giving nuclear missles to an ally. China's missles will probably be stopped by our first line of defense, then all of our missles launched in counter-attack would hit their mark...
Then only way China would survive is if Russia helped, but TBH we probably wouldn't even launch a nuke... to expensive. We could just go over there with a couple aircraft carriers and put an embargo on their trade.
Speaking of trade China needs the U.S. 90% of the stuff we buy here is "Made in China" who would blow a big cash cow like America? I know China wouldn't