The former carries a connotation of Washington DC dominating the entire Americas, IMO. Maybe it's a carry-over from my past as a TEFL teacher, but I prefer to give the rest of the Americas their independence from the stars & stripes.
The trouble is when you're describing the peoples:
Canadians (fine)
Brazilians, etc - i.e. by country (fine)
South/ Latin Americans (fine)
Americans?? err...USA-acolytes? YankeeDoodleDandies?
What say you?