Since both China and the US have the capacity to annihilate each other, they're unlikely to engage in direct conflicts. So their struggle will be more like the cold war (proxy conflicts, squabbling over allies and prestige etc) than WW2 (direct fighting to conquer land/people).

The most interesting thing about the US China relationship is that they're mutually reliant. Decoupling their economies is likely impossible and even if it weren't would take decades. That wasn't true of the USSR/US or Britian/Germany. So that adds another layer of anti-direct-conflict mechanics.

I'm hopeful that a new Cold War might see some social improvement (the cold War was a boon for social programs, science and technology funding, education and the arts). Though I think it's unlikely as China is much weaker than the post-ww2 USSR was...