We wouldn't lose, but probably couldn't "win" either. With our intel gathering abilities and various other advanced technologies, we could do a pretty good job of chopping apart their command and control structure to the point where they couldn't mount a cohesive offensive or even a coordinated defense. The usual problem of course is that "winning" doesn't necessarily mean just eliminating the govt and taking enough strategic positions to cripple a nation. Countries nowadays are willing to enter drawn out wars of attrition even when it is an otherwise lost cause in the sense that whatever national entity survives will not be the same as the one in place at the beginning of the war.
A conventional war in China would probably start with an extremely fast paced and violent assault on certain infrastructure and leadership, and I suspect that we would be successful in eliminating their ability to coordinate their efforts except for the types of coordination that could be accomplished by couriers essentially on foot. But since we're a kinder/gentler sort of nation now, we would avoid hitting civilian infrastructure and that guarantees that a drawn out low intensity conflict would be immediately entered upon the end of the first phase of the war. The average citizen would have little incentive to stop fighting so they'd keep fighting as long as they had food. Not taking out their power plants, water sources, etc. would just empower the resistance forces.
The key thing to realize is that there is no currently acceptable way to convince the entire nation to give up, regardless of the use of conventional or nuclear weapons. The more we modernize our military and make it more efficient in achieving specific military goals with less collateral damage, the more our military becomes a defensive tool. We currently possess the ability to completely dismantle the leadership and command structure of any nation on earth in a matter of days, but we do not have the forces or nationl willpower to do much after reducing the organized military opposition. Iraq is proving that even though we have fairly good intentions regarding the future of Iraq, we are simply not set up to occupy and rebuild a nation that was disarmed but which never surrendered. It's an important distinction to make and although we're persisting in Iraq out of a sense of moral obligation after trashing their national infrastructure and government, we're essentially forcing a square peg into a round hole.
