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.
)