Even though this type of war would last over a decade, with dozens of millions of deaths on both sides, the United States would win. The United States' military budget is over 5 times larger than China's. The Chinese would be on the defensive for majority of the war, the naval warfare would last less than a year with a US victory; however the land battle would last around a decade, as even though the US has better trained troops and technology, the Chinese out number them 4 to 1, and remember the Nazi's fighting the Soviets during WW2, quantity on itself can be quality. This would be a fantastic war the witness, but not experience.
And china does have a higher population, but does that mean you expect to send granny into the battlefield... No countries only send trained, well equipped soldiers in their prime (atleast super-powers). And america has a better force in quality and quantity.