I don't think there will be that much competition. Many Chinese people are fanatic about doing things that advance national image, things that allow them to feel they are avenging the humiliations of the last 200 years Unlike the Soviet Union they get modern capitalist competition and technology, and they have 3x the US population (although they are still poor per capita). The US, in contrast, is exhausted by its welfare-state commitments; the recent political theater indicates that even laughably small cuts in the entitlement state are still unthinkable. This spending is gradually going to crowd out much of what the government does. Any competition in space on our end is going to have to come from the private sector.
Unless China is a long-term illusion built on a bubble (which is possible), they will be as formidable an adversary as they want to be, and not just in space.