I've never ridden fixed, just single speed on flat land when under 10 years old. But my perception is, you might be faster on fixed because you are forced to climb out of the saddle, rather than spin up in a lower gear. The few road bike races I've seen on TV like the TdF, they climb standing. I'm faster on multi-speed that way, typically 2 or 3 gears up when standing, it's simply a question of if I run out of wheaties and need to downshift and spin, or walk up. I've also noticed more chain and cog wear since climbing while standing.