I think ‘peeve’ is more American because it’s modern American-informal from ‘peevish’ so it’s not caught on much in other countries. You’d probably.also be confused by ‘pet aversion’ which is actually the original and popular term, with a pet hate being the most slack of the two pets.

Edit: Come to think of it, I don’t think I’ve ever heard anyone say “peeve” in any other context, even Americans.