I'm not sure it's just a China-US thing. I think Europe will increasingly find itself taking a role. India too.
To clarify, while US-China superficially seem like the 'sides'. Really, what I think is happening is that the values of many (especially Western) countries around human rights, democracy, freedom of religion and expression, are coming into conflict with a new kind of Chinese authoritarianism that really doesn't care for these things and is quite willing to subjugate large groups of people in doing so (Tibet, Xinjiang, Hong Kong, claims to Taiwan, etc.).
To clarify, while US-China superficially seem like the 'sides'. Really, what I think is happening is that the values of many (especially Western) countries around human rights, democracy, freedom of religion and expression, are coming into conflict with a new kind of Chinese authoritarianism that really doesn't care for these things and is quite willing to subjugate large groups of people in doing so (Tibet, Xinjiang, Hong Kong, claims to Taiwan, etc.).