I'm agnostic: I love the fixed and I love SS. I have a flip flop hub, but it stays SS these days, as I almost ruined my right knee riding fixed. Something about the skips and back pedaling didn't sit with my knee.
Since going SS though of course I miss fixed. But unlike others, I find my 10 mile one way commute thru NY City streets to be faster on SS than on fixed. I chalk it up to having road bars and brake hoods/levers. I go faster knowing I can stop faster. Then there is the flying down the descents. And floating over rough patches on SS is just faster.
And as for hill climbing. Yes, on a small hill without a steep grade, you can do it faster and 'easier' on a fixed gear bike. But if the hill is long and/or steep, you're sunk against a geared bike. No question about it. I'm talking here, real hills, as in mountains.