That's one. The other key difference is their views on friendship and on murder. Both were conditioned towards violence in relatively similar fashions, but Earthland Beatrix had the priority of "for the family" whereas Edo-Beatrix had the priority of "for the glory" when it comes to their jobs. Earthland Beatrix talks big, but she's only ever killed two or three people and that was from assassination jobs. Not just murderous whims. Whereas Edolas Beatrix has a much higher headcount as she has not only more assassination jobs under her belt but she doesn't distinguish killing someone from beating them.

Such small differences in background have big differences in outcome. Kind of a cool thing.