Legacy characters have long been a point of contention in the comics, and when it comes to Batman, the debate only gets bigger.
Bruce Wayne is and always shall be, to many, the definitive Dark Knight. Despite the fact that other characters have inhabited the role from time to time (including Azrael, Dick Grayson and Terry McGinnis), the thought of anyone other than Wayne inhabiting the part is downright unpalatable to many Bat-fans, and while it's true that Bruce is the most iconic character to have donned the cape and cowl of the Caped Crusader, the mantle doesn't belong to him alone.
It belongs to Gotham (or in Grant Morrison's Batman INC., even the world), and it's an aspect reflected by those who've taken on the role when he's been otherwise deposed. Of all the characters to have succeeded him, however, Terry McGinnis and Dick Grayson are undoubtedly the best; the former the Batman of the Future, and the latter the first Robin and eventual Nightwing of the Bat-family.