I think the Joker comparison is more apt because Jokers origins are obscured, there is no reason he can’t come from wealth and / or training and the Heath Ledger Joker, at least, suggests the possibility of both. The Joker is all about using violence to expose the hypocrisies in society at the highest level whereas Batman is an Authoritarian Corporatist at heart (he can’t help it) and while he does fight crime, he’s is generally depicted doing so in such a way as to terrorize the lower level criminals while leaving the biggest criminals at the top in place. Even if he removes them, he does nothing to dismantle the systems that demand that people like them exist so someone else just raises to fill the place of the old boss and the show goes on.