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Who wins?

Catwoman would win. Has enhanced agility and all that of a cat+nine lives. Elektra is good at martial arts. That would maybe be the only pro for Elektra. I'm not sure who's more smarter. If Elektra did, then she may win.

Sorry rainbow, but you're WAY off. Catwoman isn't enhanced anything, you must be thinking of the movie. Catwoman's good, but Elektra could definitely show her a thing or two.

I love Catwoman, but Elektra would win this. In terms of pure martial ability Elektra is beyond the abilities of Selina Kyle. In terms of DC (human) women i'd say the ones who could take Marvel's Elektra are Cassandra Cain (the current Batgirl), and obviously Lady Shiva. But Catwoman would have no chance.
Onyx (the crazy martial artist who trained for years at the same monastery that Green Arrow briefly called home) might give Elektra a good shot, but i think Elektra would beat her after some moves.
Elektra is the quasi-Lady Shiva of Marvel, and the Catwoman is just not at that level. Neither is Huntress, the old Batgirl (Barbara Gordon before she got crippled), and Spoiler would also fall fast and hard before Elektra. The current version of Catwoman is better than Huntress, far better than the old Batgirl, and ridiculously more adept than Spoiler; but again she is nowhere near Elektra.
Unless the fight involves jumping from building to building on ropes and lines and grapplers, in which case Catwoman would win, Elektra would kick Catwoman's BEAUTIFUL behind.
Again, only the current Batgirl and Shiva Woosan can beat Elektra. The other women are outmatched.
Catwoman goes down.