St Andrews is old and not “red brick”, which made it appropriate for Prince William and also attractive to Americans. The US does better in University rankings, as almost all instructors have PhDs and there is an emphasis on “publish or perish”. St Andrews is comparable to a fairly competitive school in the US, although maybe not to Ivies.
IMO Americans are at a disadvantage applying to UK Universities, because they haven’t concentrated on 3 subjects and preparing for exams.
As for OP’s plans to study humanities, those programs are in some ways better in the UK and Europe in general. The degrees are more respected and marketable than in the US. However, there is some disadvantage in returning to the US in that US humanities majors will generally have taken some courses in more “practical” areas.