She's faster, but especially later in the game, Batman simply gets a lot of incredibly useful takedown maneuvers and gadgets, like a move that disarms an enemy and also destroys the weapon in the process. He can also disarm enemies from much further away and gets a freezing grenade that takes an assailant out of the fight for the entirety of its duration. Catwoman can disarm enemies as well, but usually the dropped weapon gets picked up by another guy as soon as it hits the floor. Batman also has a good deal more health and his special vision mode separates between regular guys and guys with firearms. He can even disable weapons before the fight even starts. And if everything fails he even has a get out of jail free card in the form of smoke pellets.
Then there's all the other benefits: his grapple has a far greater reach so he can zip instantly to a nearby rooftop or gargoyle. He can even surpress his body heat when he's up there, and of course he gets around the city much quicker.
Don't get me wrong, Catwoman is a ton of fun to use (if only to watch the animations) and I agree that it's easier to take out large amounts of low level thugs with her using basic maneuvers, but as soon as the game introduces guys with tasers, guns and shields, Batman becomes a lot more effective.