The Joker wanted Batman to kill him.
"You just couldn't let me go, could you?"
If Batman had let him fall he would have won - succeeded in proving his 'sick philosophy' was correct.
BATMAN: I have one rule.
JOKER: Then that's the one rule you'll have to break to know the
BATMAN: Which is?
JOKER: The only sensible way to live in this world is without rules.
And tonight you're gonna break your one rule.
It probably would have been more sensible to kill him, given how dangerous he was, but that is precisely the unprincipled utilitarianism the joker is espousing. After the incredible bravery of everyone on the ferries defying the Joker's game, it would be poor form for Batman to immediately give in to it.
Batman is better than the Joker ("more than just a man") because he has his rules - what kind of message does it send if the symbol immediately abandons them when it gets a little tough?
(Or to put it another way, Batman wasn't 'just' trying to save the city like with Al Ghul - the Joker entered into a massive scheme to tear down the belief in things Batman stands for, so Batman has to fight back accordingly (and makes the ending very ironic!))