Dice is definitely a conflicting character in comedy. He was the absolute king of the scene for a brief moment in the late '80s, early '90s. Heck, he's the first guy to sell out Madison Square Gardens two nights in a row. And then he just really fell from the scene and is now considered one of the worst comedians of all time.
Which I find really unfair. Some time ago, I had heard a list of the Top 30 Stand-Ups of all time, and was really impressed by Rodney Dangerfield. I went on YouTube and looked up his material, and was like, "Yeah, he's pretty great." Then, on the sidebar of other vids to watch, there was "The Diceman Cometh". I went, "Hey, this guy was on that list too... I think I'll check it out." So I did and I was just blown away.
I'm not usually one for sex jokes, but Dice's persona just makes them side-splittingly funny. I don't think he gets his due these days - he pushed the boundaries of comedy, as stated above became the first to sell out MSG twice in a row, and everyone who was around when he was on the scene (and with an interest in comedy) remember him. I've said to people before, "Hey, you like comedy, ever heard of Andrew Dice Clay?" and they'd respond with a laugh and go, "Oh yeah, The Diceman!" Dice was big, and I'd say that he's the best example of a comedian 'rockstar'.
Yes, Dice did fall from the scene quite hard, but even after his 'fall' he made at least two great specials, Assume the Position and No Apologies, and even his more recent work has been funny on occasion. Whilst I admit, nowadays he's a washed-up celebrity has been who can't except the fact that his heyday has long since been over, for the material he put out in his peak, he remains my second favorite comedian of all time, behind only Carlin. He's not a comedic genius like Carlin or Pryor, but he was able to take sex jokes and misogyny, create an offensive, crude, brash character who said all the most un-PC things possible, and get away with it, uniting both sexes to enjoy his comedy.
That, in my opinion, is what made The Diceman great.