I've recently (this September) introduced my girlfriend to RPGs, to Shadowrun in particular; I'm currently running a one-on-one Shadowrun campaign for her. To tell the truth, she has alot of gaming potential - she got the basic concepts (getting into character, PCs vs. NPCs, roleplaying) very quickly, faster than most male gamers I know (possibly due to the fact that she's started gaming at the age of 22, not 12). Initially she was scared by rules, especially ones with mathematical aspects (she has near-PTSD from VERY hard differential-calculus courses in college), but once I've managed to calm her down, she've grasped Shadowrun's complex combat system faster than most male gamers I know. I haven't played with her in larger groups, but I don't think she'll even WANT any kind of favoritism - she's quite into game-world consistency and realism, and builds her characters according to their backstory, which is not munchkinish.
All in all, I think that it all boils down to the DM's and GF's individual personalities and tastes rather than any overall gender tendencies.