I didn't see if anyone mentioned it, but word of god on Leto's Joker is that the "tattoos" were only part of the promo shot. They're not in the actual finished product.
I still stand on record as always feeling ambivalent about Ledger's Joker. I also didn't feel like he represented the Joker. I understand as a huge comic book nerd that the Joker has gone through many interpretations, but that's just it. Ledger's Joker had no real distinctive features or personality. He just read like a generic movie psychopath, and where's the fun in that. As someone else said, he did that role very well, but there was nothing uniquely Joker about it.
I mean, saying a character is something just because you call it something is probably technically true. I guess any old rich kid from Verona could be Romeo, forget any plot actions or personality cues from the play. It's Romeo if you say it is, right? Technically, I guess. But that still extremely unsatisfying, and fans of the original play have plenty of justification to complain about it.