The Batman that cares about the inmates is my favorite. He doesn’t put up with their shit, but he does try to reach out here and there and he’s as human as he can be to them.
When Harley was re-institutionalized, he got her that dress she wanted.
In the comics based on B:tAS, there was a time during Christmas that there was snow and it was Mr. Freeze’s fault, and he was making it snow because Christmas was his anniversary with Nora and she LOVED it when it snowed on Christmas, so Batman let him finish mourning before calmly taking him back to Arkham.
He never, ever gives up on Harvey possibly recovering.
Sure, Batman is going to throw punches and do what it takes to take these guys down when they’re hurting or threatening people. And he’s not going be a complete bleeding heart; he has to protect the innocent. He’s going to take them down and take them back to Arkham, but it doesn’t mean he’s incapable of being a bit human to the ones who deserve it.
Honestly, I was able to feel for the Gotham bad guys because of the way this show presented them. It’s all down to the writing and the voice actors.