I think China would be more than happy if the US would be reduced to being an equal . Not that the US is superior in everything, but China sees the US acting and thinking that way.
One thing that I think China has to face and deal with is a looming ecological nightmare from their rapid economic expansion. I believe this is maybe their greatest looming problem.
Another problem China would face if they wanted to be a global hegemon like the US is their location on the map. The US is geographically located in such a way that enhances its global position in the world.
Bobcat