Perhaps an overly broad question, but I’ll give it a shot. Is the US culture, whatever that may be, superior to some other cultures? Undoubtedly; for one thing, why do more people seemingly want to emigrate to the US than any other country? Is the US culture ‘better’ in some fundamental sense, than all other cultures? I think not.
Of course this was not always the case, but I think most European countries since at least WWII have cultures that are more compassionate toward the poor, better appreciate the arts, and are far less violent than that of the US. OTOH, it is clear that in some European countries the class structure is much more evident than the US, with seemingly much less career and social mobility.
We are told that certain Asian and African cultures tend to place a greater emphasis on the family. On the other hand, can anyone look at the political and/or social cultures of countries such as Liberia, North Korea and Libya (to name just a few regional examples) and argue that there is much worth emulating?
Some of the things I think may contribute to an assumed superiority of US culture: more or less democratic political system (shared by most European and some Asian countries), broad internal freedom of movement, freedom of career change, flexible class structure, entreprenurial spirit, relative lack of political corruption, generally secular political and social system, economic structure that rewards individual initiative.
Some things that take away from that potential superiority: high level of violence, increasing militarism, relative lack of compassion for the less well-off, poorly-structured social support systems, anti-intellectualism, relative lack of understanding of other cultures, economic structure that tends to marginalize large social or ethnic groups.
Hope this is the sort of thing the OP was looking for.