In BTAS Batman was angry and intimidating at times, but yet he was still often a "nice uncle". He even made some funny remarks ("Let go off my cape", "I'll drive REALLY slow", Catwoman "I think there is something between us?" - "Yeah, I think it's the law", "I take it out of your salary", "garbage collection is usually mondays"). Even in Nolan's take he is like that.
In JL he is more like the 90s/early-00s comics all the time. As I put it: Unlikeable. Cannot understand why this guy has fans. I mean, look at the episode where the JL members become kids and Wonder WOman asks Batman if he likes it to be a kid again and Batman answers something like "I've never been a child since I turned 9" or something similar. C'mon, THIS is the guy who had a "Grey Ghost's Lair" replica in his batcave in BTAS.