Originally Posted by pr0xyt0xin
But he had time to save the Joker from dying in a very similar manner.
No he didn't. Joker fell by himself. Batman fell with Dent and Gordon's son. He could only save one or the other. Not both.
With Joker he clearly strategized the attack to graze his face with those wrist blades ("No, but I know how you got these"), then throw him off the building, then catch him with the grappling hook. That was an obvious planned strategy.