and OP, if you're not seeking financial aid as an international, you're still gonna have a hard time compared to domestic applicants i.e. higher SAT scores, better ECs, better stats etc. but if you're comparing colleges, then of course, the best of the best colleges like HYP will be harder to get in than the rest of the best colleges like Cornell, UPenn, etc.
LACs are a whole different category. they all generally have very small classes and thus smaller room for internationals - so you can't compare them with big research universities.
yeah, unless you come from an underrespresented country like Greenland

Are the Swiss underrepresented in American colleges? Having addresses in two countries is still pretty cool though, only if you milk that experience for what it's worth i.e. essays, interviews