I'd expect China is worse off. President Richardson mentions that the Chinese were the first to launch their ICBMs at America shortly after Alaska was liberated, so in turn the Americans must have send theirs out shortly after the warning, plus due to the Chinese instigating the attack, anyone in alliance with America (UK, etc) would have fired their nuclear weapons too and probably hit them back twice as hard. The Fallout timeline mentions that every capable nation joined in the 'Great War'.
Well it hasn't really been determined who fired first. President Richard said some things, that could be taken as either truth or just propaganda? So it could have been a unknown simultaneous attack, either side not knowing the other was firing when they were, until the alarms went off. So China could have been hit just as hard, assuming that Russia was an Ally of China (which isn't really known either.)
But like I said, most of mainland china is empty space, and most of their metropolitan areas are along the Yellow Sea, and South China Sea.