I see the US and most Western countries as more individualist, liberal, democracies. China is more of an authoritarian, collectivist, technocrat model.

These models reflect moral as well as political beliefs. The models are also not compatible - meaning we can't be both and the more of one the less there is of the other. This is the sense in which we have conflicting views and are striving against one another to promote our ideology.

> not that the domain of morality is a piece of the competition in the domain of global mind share

Haven't the 'best morals' always have been those with the most mindshare ?

The best morals are the ones that not only spread, but also persist. Morals that preserve and promote trust and cooperation tend to win in the long run.