There was an old QI segment (UK panel talk show hosted by Stephen Fry) where someone remarked about Costner's accent and then someone else said "I can't imagine it'd have been a better film if he'd been struggling with a kind of Dick Van Dyke cockney accent!"
I would easily take Men In Tights over Prince Of Thieves. The Rickman parody in that movie is a laugh riot even today.
It's sort of weird to me that people are even still watching Prince Of Thieves. It was a big hit and I guess there are poor dupes out there who still like to hear that Bryan Adams/Rod Stewart/whoever song.