China's birth rate is much lower than the US, but both are below replacement. US is only slightly below. India is slightly above, but falling.
IMHO the countries to dominate the 21st century will be those that attract the largest number of high quality immigrants. Countries that do not will stagnate. Countries that drive quality people away (brain drain) will collapse.
The US has an huge advantage there unless we stupidly close our borders because of racism and fear.
China will fare poorly if rising authoritarianism and low birth rates lead to both declining population and population loss. Nobody migrates to authoritarian countries unless they have nowhere better to go and are fleeing something a lot worse.