Benefit of a fixed gear... none really other than simplicity. It's a road bike setup with less shit to break, but you get no on the fly gearing options and never get to stop pedaling. I went fixed gear to get my legs in shape, and in three months I'm where I wanted to be.
I'm going to be putting gears on the frame I'm currently using, but I'll just get another frame for all my FG stuff.
It's nice knowing that the only thing that could probably go wrong is a flat tire. I could break a chain.... but probably not. It's got a good feel through the pedals too IMO.
There is no real practical advantage to a fixed gear.