There's a Birds of Prey arc on this. As Batgirl, Catwoman was one of Babs rolemodels. Catwoman comments later to Oracle (not knowing that they are the same person) that she really could use the original Batgirl as backup and that she really respected her fighting skills. Catwoman was shown as slightly more graceful than Batgirl though.
But are we talking Batgirl or Oracle?
If it's against Oracle though, is this a long distance fight or does Oracle have prep? (If she has prep the same rules as Batgod apply. )
Batgirl not Oracle. Without prep. I think prep won't be a factor against Catwoman since she's been giving Batman hard time and her specialty is getting out of sticky situations and saving not other people but just herself. So this is just about fighting skills with weapons.