The enemies say he's batman because they think it's batman, just like in the very beginning of the game when the enemies think catwoman is batman. If you play the iceberg challenge map, penguin doesn't even know nightwing's name.
They can't give them similar moves to Batman, because there is only ONE B-Man. That is what seperates the characters and their move set form each other. Otherwise you would just be playing the same thing with a different skin. I find that Nightwing fights
a lot slower because of his sticks. It forces you to use different tactics when coming up against armed fores rather than just disarming them like Batman; and let's face it, Robing, Nightwing nor Catwoman posess the strength to break a weapon.
Personally, I think Nightwing is great for actually learning the combat system for people who aren't familiar with it. Like Mamba said, Nightwing is slower than Batman and Catwoman which makes it a heck of a lot easier to counter enemies' attacks because
you have so much more time to do so. I do agree they should have added the weapon break move. It seems like they really just wanted to get Nightwing out as quick as possible. What they should have done was release Robin first and then Nightwing months later.