Earlier quoted context omitted.
The practical part of space flight is launching satellites, and weapons. Both countries are already doing both. If we're discussing manned missions to the moon or Mars, as an American I'd prefer China spent all the money and the US didn't bother. It'd be cool to see it happen, but no one can identify practical benefits, aside from a political win.
You are missing that the money and research into figuring out how to solve many engineering and scientific challenges related to the missions had tremendous benefit to industry later. As we gain ability to do my re in space more cheaply it will get more important
The economic cases for manned moon or Mars programs look really iffy these days. The US has poured tens of $billions down the SLS rat hole, with very little to show for it. And Wienersmith's A City on Mars is a pretty damning dissection of the whole concept of Martian colonies.