Interesting.

Both are criminal geniuses, but the Joker is too much a thug to prevail over the suave and cultured Doctor.

My vote goes to Hannibal.

Truth be told, Hannibals air of culture and sophistication would be completely useless on someone like the joker. It works on regular people because they view those qualities as friendly and disarming whereas the Joker would see right through it or just wouldn't care.

They're such different characters. Any sense of wisdom would point to intelligence winning over psychotic mayhem. If someone could write a convincing script, this would be a fantastic idea to build upon.

Yeah, everyone's right, Hannibal would win hands down. He can get him both physically and mentally. And who better to understand the Joker than the genius psycho psycologist himself? And with understanding comes the advantage of predicting one's actions :)