This has been proved somewhere (I can't find it), but from experience I know it to be true:
A fixed-gear drivetrain has a distinct advantage on hills. Your cranks are coming around behind you, helping out on every revolution. For all but the most murderous hills, this actually makes it easier to climb on a fixed gear. (It doesn't mean that you'll always be in the gear you want. But you will hit a groove and blow by almost everybody else on the hill.)
This is not true with a freewheel. Climbing the Manhattan Bridge on a singlespeed with a tall gear (say 48x16), frankly, is a drag. HOWEVER, if you ride in heavy traffic and have ever found yourself picking your way between a car and a curb, it's nice not to have to keep turning the cranks.

Both are great commuting bikes, but fixed gear is more of a game in traffic, and a very fun one. It's also cooler, which is why so many singlespeed riders foolishly opt to dump the rear brake, I guess.

Go with the flipflop hub, as many suggest, but I bet once you get accustomed to the fixed side, you won't go back. I didn't.

A word about skidding! I was very proud to have taught myself to skid. Very impressive and a great skill to have in an emergency. Unfortunately, my gear ratio was 48x16, which left me with exactly one skid patch. Meaning that I essentially wore down my tire in the exact same spot with every skid until one day, the tube was almost bursting through the tire's fibers like an aneurysm.

Good luck.

PS: As for the people who feel that a freewheel feels broken after riding fixed? Alas, it's your pedal stroke that's broken. You've become accustomed to the cranks kicking your feet around rather than doing it yourself.