The whole story between Batman and The Joker (at least in the Dark Knight books) is that killing a person is the one line Batman won't cross. He won't be a killer. Hurt them? Yell yes. Scare them? That's the entire point. But he won't kill them.
The Joker is always his purest nemisis, because he won't stop until he is indeed killed, and by Batman. As he said in this movie - it's the irresistable force versus the immovable object. It's Yin versus Yang. Good versus evil. Bruce can't let himself become that, and ultimately The Joker knows that. It's his Ace up the sleeve - the kryptonite to Superman. He has figured out the true Achilles Heel of Batman. It's also really cool. You have a crazy killer who is being hunted by a crazy vigilante only the latter won't cross the one line he knows he must to stop the former. Great, great stuff. In the real world, yeah, he would get captured and locked up and never get out. But in this world, he always escapes - constantly pressing Batman. The argument is that neither can exist without the other.
Even in The Dark Knight Returns - when the older Batman finally realizes that he must in fact kill The Joker, he can't bring himself to do it. In the end, he finally compromises, and severs his spine (in maybe the best comic book series ever written).