China (and Russia's) disadvantage is that they are autocratic nations that don't play nicely with others. The West's advantage is its alliances. If the U.S., Canada, Australia, Japan, Europe, etc. all move in lockstep, autocratic nations can't ignore them.

You talk about a cold war as in specifically U.S. vs China. If it is just U.S. vs. China (meaning the U.S. isolates itself further from its allies in the future), then the U.S. will lose. China has a quarter of the world's population, heavily invests in science and technology, and has a population that is intensely nationalistic and works its ass off. The need for self-censorship and the cultural resistance to individualism means that the Chinese will always struggle in the arts, but that's about it.