I like 'em both, and sure can't improve on Poguemahone's essay.
I like my fixed gear in "fixed" mode on my trainer, to the convenience store and back, and on carefully planned "out and back" rides where I go 15-20 miles out in fixed, then flip-flop the rear and ride back with a freewheel. My bud calls them "rip and recover" rides.
For everything else, I like geared bikes.
I've seen some crazy dudes on fixed gears doing near-BMX stuff on Cinelli track frames.
I'm glad they're on bikes.
This is about bikes, right?