I didn't see the show on Broadway, but the Broadway cast recording gets the music quite badly wrong. British pop music of that era, including Culture Club, is characterised by a combination of slickness and artlessness. The Broadway arrangements are a little bit too smooth, too glossy. They take a score that in London did quite a good job of evoking the show's milieu and render it bland.
And also the accents from everyone who isn't British are laughably appalling and the keychange-too-far that's shoehorned into the Broadway version of Talk Amongst Yourselves brings new meaning to the word 'bathos'. The London show wasn't perfect, but the Broadway album is almost unlistenable.