China is on its last legs, what we are seeing is the finale of the communist middle kingdom
My opinion is that it's a race to see who outlives the other.
The US is currently being forcibly arranged into a corporatist Anarcho-Tyranny, but immigration will still sustain it for quite a while, at the cost of its national cohesion and identity (currently being demolished by the underemployed aspiring elites of the country). It still possesses a massive headstart, in terms of its amount of reach around the globe, as well as a culture and economy that allows it to innovate when it comes time to push (at least until the woke fully penetrates).
China on the other hand faces a demographic echo as its vast middle-aged population starts to reach the end of their productive age, and is racing to innovate and avoid the middle income trap- but it possesses a huge amount of political and national cohesion and identity, in no little part due to the nature of its totalizing government. However, that same government likes its perpetual """6% growth rates""", pointless international sabre-rattling, and also stigmatizes any sort of whistleblower culture that builds resilience and real innovation.
IMO, the pandemic and vaccine race illustrated this well.
In general, China has around 20-30 years to get this sorted out internally while the US races to contain them globally before that- whether or not it can get it done depends on how much cohesion it can muster in itself and its allies.
Secondly, continued automation + AI improvements running into the next two decades may continue to reduce the size of the population needed to run the economy as well. I don't see the CCP ever accepting mass immigration as an option, as they would see it as an affront their pure-Han space. In the end, it all boils down to this phrase-
"Can China become rich (and automated) before it gets old?"