I think it depends on the nature of the fight.
If you're asking who could kill who, then the answer is obvious. X-23 wins. She can't be killed.
But if you're asking who wins in a fight, or who incapacitates the other, then Batgirl wins. She wins for the same reason Cap opens whupass on Wolverine. In a fight, the superior fighter wins. Wolverine and X-23 are basically brawlers. They don't need to worry about style, as they will heal if they're hurt. But fighters like Cap and Batgirl will win with superior skills. You can't beat 'em, if you can't touch 'em.
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