The challenges are plenty, but I'm confident China can deal with most of it.
The only aspect I worry a lot about is demographics. The forces at play there seem beyond most countries' ability to control; and East Asian countries, especially, have not found the way to do it. Look at Japan. Look at South Korea. Basket cases in demographic decline.
If China can solve the demographic problem and go back to a stable or growing fertility rate, I'd say the future is bright regardless of what the US does. China just needs to wait it out, until the forces of history equalize the playing field. But at the current speed of aging, time may in fact be on the US's side. It's very hard to beat the US - which keeps importing young immigrants - if half the country is 65+ and the other half is stuck in service jobs because of it.