The United States of America would win.
We have Falcon HTV-2 hypersonic planes (can travel up to Mach 20) - the fastest in the world, traveling 20 times faster than the speed of sound. It can travel from Sydney to London in 1 hour (normally a 23 hour flight). These planes can travel from USA to China in about 35 minutes. The fastest cruise missile in the world are supersonic at best and no match for hypersonic planes. The Indian-Russian built BrahMos missile travel at Mach 3 at best, no match for a Mach 20 hypersonic Falcon HTV-2.
Added to the fact, China do not possess a BrahMos and at best have substandard Tomahawks, which are subsonic at best. This means that within 35 minutes we can get planes over Chinese air space that no missile or other plane can intercept, no land weapon can attack either. With this speed, with can destroy China's nuclear power plants and reactors (our satellites can track every active nuclear weapon through heat monitoring), thus the Chinese nuclear threat is eradicated
Next, our navy is far more powerful than China's. We have 11 aircraft carriers, China have none (though they are in the process of building one right now). We have submarines that can go untraceable on radar's and torpedoes which can destroy most China's warships. We would probably take over the South-China sea within 16 hours. Our 11 aircraft carriers would surround China in vantage point, and with our Falcon HTV-2's up over Chinese airspace, our aircraft carriers will release F-16s, F-117s and stealth bombers (e.g. Northrop Grumman B-2 Spirit), would dominate air force of the People's Liberation Army. We would have complete and total air supremacy of China within two days. This will enable us to get our ground troops on Chinese soil. With the planes backing up the troops, the People's Liberation Army has no chance. In less than a month, the entire PLA would be destroyed. The Armed Forces of the United States of America would control all of China.
Also, in the event that China does go nuclear (which they wont because our HTV-2's would have demolished all nuclear resources), we have LGM-30 Minuteman's which can travel at Mach 23, the fastest, most effective and powerful nuclear warhead on the planet. The Chinese stand no chance.
End result: Comprehensive American victory.
Chinese casualties would be in the millions, America would lose fifty thousand at most.