Nope, having a male or female char will make no difference, the only thing that will make a difference in the early levels will be if you're Guardian and your friend is Defiant, each have a different starter zone and the first two zones are quests only for each Faction.
Even later as both Factions quest together in the same zones, each story line and most quests are entirely different, at least up to level 50, after level 50 to 60 most of the quests will become the same with just a few different ones.
I'm afraid i can't think of another reason why your friend can pick up lower level quests except if they're early quests on the Cult Saga quests? Try and find out the names of the quests, i mostly play Guardian so not too familiar with Defiants side, especially their Death Saga quests, assuming you're Defiant.

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