It's very interesting seeing the difference between versions. In a modern game ported across multiple platforms, they remain identical barring visual fidelity. In specific cases like the wii, they outright had different games accommodate the weaker hardware and control scheme, usually for the worst.
Here, numerous smaller but sensible gameplay tweaks elevate it above the Master System version.
For example, in the Master System versions the combat, which consists of firing battarangs was by and large, easy, it projects half way across the screen with enemies remaining largely passive until later stages where challenge ramped up somewhat.
The most noticeable different from the onset, is the battarangs distance culled. forcing the player to move in much closer to the enemy, who typically charges at the player. Sometimes two at a time. This becomes noticeable difference as well, enemies largely sat around around waiting to be picked off on the Master System, on the Game Gear they redesigned with much more intent.
For example, the Master Systems bog standard gun totting enemies would drop with one hit, while now they three, while advancing towards the player. Likewise, a gymnast enemy would jump around map, now aside from jumping around the map, several projectiles are released. Several other enemies that didn't appear in the Master System also make an appearance. In general, this seems like they examined their game and revised it, which is admirable, espcailly for a movie game. There is a sense they cared about the product, which can't be said for a great deal in this day and age.
The Game Gear version seems to have more variation in it's color pallet, the Master System was predominantly cool blues, while here Batman himself is clearly grey, with backdrops and enemies coming across as more vibrant. Wither this is better or worse, is debatable. A few other visuals effects not on the Master System version are noticeable, such as weather snow effects - (the movie taking place on a white Christmas, it's more authentic), it's a neat little effect, however archaic. The only downside seems to be shorter, segmented levels compared to the Master System version, which was probably an unavoidable compromise.
Bosses are more or less the exact same. Although as mentioned, the limited range of player projectile changes things up somewhat.
Also changed is the 1 hit one death from the Master System version, with instead a health pool and pickups regenerating health, as opposed to an abundance of player life. It suits the gamer better, it's at once more forgiving while also giving health in much needed moderation.
This is another one of those interesting adaptations to a Game Gear where it is familiar yet tweaked as to give the game it's own identity.
