The costume element aside (because that ultimately has nothing to do with liking or disliking period dramas), Age of Innocence is actually a very good film. Let's be honest, Scorsese (unless we're talking about the appalling Gangs of New York) doesn't make bad films, and period drama or not, his films are always worth watching. To dismiss all period dramas with an immature 'Period dramas suck' completely ignores all the many excellent period dramas out there - Gone with the Wind being one of the very best.
"He may look like an idiot and talk like an idiot but don't let that fool you. He really is an idiot."