My female Courier did one of two things: Either she led an independent New Vegas to be a successful state amalgamating the authoritarian effectiveness of the Legion with the rule of law and egalitarianism of the NCR with neither the brutality or corruption of either, respectively currying favor with both the Legion and NCR to play the buffer-state to either, but being sure to keep her laser sighted, expanded magazined, silenced 10mm pistol handy. Just in case.
or
She sided with Caesar's Legion and allowed them to push west across the Colorado to secure the Mojave as the new frontier, but set the example of a strong, independent woman utilizing the technology of yesterday's world, with a scoped laser rifle on her back, to force Caeser and his Legion into realizing they were wrong about a great many things. Especially after a silver coin with her face on it is spread east, she is able to work with Caesar to reform the Legion into something closer to a true, post-apocalyptic force for the betterment of humanity
I guess it just depends on which weapon skill I tagged

I have trouble siding with the NCR as it feels as if they're recreating too many of the Old-World mistakes