You said you have an affinity for the Burton version. By comparison, that version is very campy - at least as far as the Joker - goons all wearing the same jackets, driving around in green and purple cars, Joker having a green helicopter with a big Joker face on the side. Joker was reduced to being a mob thug with a gimmick.
Nolan's Batman universe is as realistic and modern day as possible within the limitations of the concept. All of Batman's gear has a logical origin - he didn't just invent it on his own. His fear of bats and the events in his life that drove him to becoming Batman are all very plausible. Joker's origin is never explained (he changes his story every time), and he truly is crazy, but what he finds funny has a "black humor" element to it. Tell me you didn't simultaneously laugh and cringe at the pencil trick. Go back and listen to what he tells Harvey in the hospital room.
"The mob has plans, the cops have plans, Gordon's got plans. They're schemers, trying to control their little worlds. I'm not a schemer. I try to show the schemers how pathetic their attempts to control things really are."
By his definition, the people who are trying to force conformity on the rest of the population are the true "crazy" ones, the ones with "God" complexes. By comparison, he's just running on instinct - "Y'know what I am? I'm a dog chasing cars. I wouldn't know what to do with one of I caught it. I just do things."
His bit with the two boats at the end was brilliant - if the convicts blew up the civilians, the convicts would be no better off than they already were and a few hundred people would be dead. If the civilians blew up the convicts, you now have essentially 400-odd people who agreed that mass murder was acceptable, thereby becoming criminals themselves. Talk about a no-win scenario.
To really appreciate the Nolan Batman films, you have to look beyond the superhero surface. Get into the characters' minds, learn WHY they are the people they are.