While I prefer the NES game based on the first movie, I think that this SNES game is the one that comes closest to making me “feel like Batman” while playing it. There’s something utterly satisfying about going through the Red Triangle Circus gang Final Fight-style.
I really like the Sega Genesis Batman Returns too (I was a Sega kid so I rented it a few times) but it’s a very difficult game. I liked how a lot of it took place in the rooftops of Gotham and utilized more of Batman’s gadgets. It didn’t synthesize the Danny Elfman score but it had some interesting original music like the Sunsoft Batman games did.
The Adventures of Batman & Robin on Genesis was pretty solid too. One of the few games I remember actually convincing my dad to play.