I usually see myself as something like a guiding spirit for my characters. I see them as persons in their own right. I don't think of any of them as "me," but sometimes I feel like I'm them. What I mean is, sometimes I feel like I'm "in their heads." I react to things as they would and can "hear" their thoughts. What I'm actually doing is writing a fantasy novel in my head as I play, so they need to have their own motivations and stuff. Sometimes they can surprise me. I feel like I understand now what authors are talking about when they say their characters have lives of their own.
I do find that I am more separated from my female characters than my male ones (I'm male). When talking about them, I usually say "she did something," but if it's a male character I'll more often say I did it. Possibly because I play the females more in 3rd person. Yes it's so I can look at my pretty girls and watch their butts.

Although I am playing my new Altmer guy in 3rd. I gave him the heaviest body type, and he's so gigantic that I enjoy watching him clomp around.