Best on flat surfaces IF the gearing of the bike is TOTALLY TWEAKED to the rider's fitness and ability.
This morning I took my new Giant out. I have a 6.5 mile loop that I do which is a combination of flat and modest hills. There are no significant hills on the route but I am sure I shift gears at least 20-30 times. Even though I am far from the picture of fitness, I pass everybody else out there fairly easily. Unless Greg LeMond or Lance Armstrong show up on my route, I cannot imagine someone on a fixie riding it faster.