Excellence is the highest standard - the true Wonder Woman is the best Wonder Woman
Fair enough, when trying to decide "what the real" version of a character is. If somebody asks me to write "a Batman story," totally divorced from all other considerations, I am naturally going to use the Batman who is closest to the platonic ideal, something that resembles DCAU or Bronze Age Bruce, something like a genuine hero.
That doesn't solve the problem of "what version exists now," however. Paranoid, insane, emotionally stunted, hostile asshole may be OOC for the ideal, "real" Batman, but given the (essentially) coherent DCU, it is not out of character; it can't be. Ted Kord is still dead. War Games still happened. Sasha Bordeaux is still half OMAC. Cass is still... well, okay, Cass is a whole other issue, but you know what I mean. As long as these things are still true, Bruce still did those things, which means a consistent and repeated pattern of behavior exists, which means that that character is still that character.
Maybe the "real" Batman isn't like that. But DCU Batman is.