This is my main issue with Catwoman. For her to be interesting, at least IMO, you would have to take this approach, but it's already been done, and in numerous ways.
Ras was a dark mirror to Bruce Wayne. He had a similar experience, but instead of fighting crime within the limits of legality, he takes a more vindictive stance, while still using the same techniques.
The Joker was a dark mirror to Batman as well, as he always is. Where one is stoic, driven by a specific goal and mission, and entirely serious, the other makes a mockery of being specific, or having any morals or code. He uses theatrics just like Batman, presumably, exists
only because of Batman, and judges himself against the competition with Batman.
Harvey could also be seen as a mirror of Batman in terms of duality. Once again, we have someone who endures a horrible experience, and becomes two different individuals disenfranchised with the system because of it. Not only that but Nolan's version is made to represent that mirror even more with his relationship to Rachel, and more prominently, being seen as the "White Knight."
I just don't see what would be new or different about Catwoman besides the fact that she's a female, and as we all know, we absolutely must have a female lead