I, personally, would have used Batgirl as they've already ( Sort Of ) introduced Barbara into the Nolanverse and it would've made a stronger connection between Commissioner Gordon and Batman if Gordon's daughter was Batman's sidekick. She was obviously just a child in The Dark Knight but Dark Knight Rises is set eight years after the second film.

Of course, there are plenty of good reasons to use Catwoman, she is a well known love interest for Batman and it sort of shows Batman having more emotions.

Which of the two characters would you have used and why?

Catwoman>>>>>>>>>Batgirl

Batwoman

Cause I'm a rebel.

Batgirl has no place in the movie. Catwoman was at least somewhat apart of Knightfall.

Catwoman. Batgirl is somewhat annoying to me.

I wish batgirl was in it so she can stop bane and released inmates