Actually the 2 needn't be in conflict. Your portrait should give the viewer a sense of the real you while still showing that you take pride in your appearance. If I shoot your portrait, we'll first ask "Why?". Is this a presentation of you for general use or should it be shot with a particular situation in mind. To exaggerate what I mean; Are you applying for a job as a rodeo clown or a mortician?
Recently I made some portraits for Mike Klein, the General Manager of the Eliza Jane Hotel, a beautiful smaller hotel a few blocks from the French Quarter. Having looked at the shots of other G.M.s in the group I started with something similar to the others.
Mike is a pleasant, relaxed guy, I wanted to show that so I asked him to have a seat. We got a shot in which, I think, he looks more like the relaxed, friendly person I met and chatted with before I started shooting.
We liked the more relaxed look so I asked Mike to lean against the bar at the Eliza Jane.
To my way of thinking, after talking to Mike about things like kids and the hotel business, the last 2 shots give you a view of him that reflects his personality while still looking just formal and posed enough for the intended use.