Well, first things first. This is a fun post, posted in forums that its main audience is from The States, so of course the answers you gonna get ain't even close to reality.
Such a War would turn into a World War since we are talking about two Super-Powers of our ERA.
In a Nuclear War noone would win but the consequences would be terrifying for the Humanity.
Now lets go to the other part: A non-Nuclear War... I've been reading some posts in here speaking about USA Defensive system and how much money has been spend into it, same goes for the USA Army in general. Well thing is we are talking about 2 different countries mentality wise. America is pro-news on those matters and its "democracy" allows its citizens and the world to see the money that has been spend in the army and defense mechanism in general, while China which is a close communist country open to Capitalism in its World-Wide trades never announces or actually has Showed off the money that they've spend building their army, or training it.
That been said, if you compare the facts you already have in your hands you'd get the correct outcome:
USA Army: Well trained army, with experience in actual Wars. Technology wise: Good. Total population of the USA army during 2012 = 798.000 soliders including Air Force, Navy and Marines.
Chinese Army: Training unknown at the moment, experience in War: Thousand of years before. Technology: Definately Unknown. Total population of the Chinese army during 2012 = 2.300.000 soliders.
Hmm with all that combined seems like the Chinese army is more likely to win with having almost triple the army that USA has. Also we are talking about two different mentality countries, where in USA you have rights as a Human being and as a solider you are not treated as a piece of meat. While in China under its current political build if you do something wrong within the army (training etc) they have no remorse of chopping you off turning your skin into soap.
Yep sorry my fellow pro American friends, the American army wouldn't even stand a chance against the Chinese army without nuclear weapons