You're thinking about it too much.
Buy a fixed gear. Ride both bikes. You'll find you'll have periods where you prefer one and periods where you prefer the other. Eventually, you'll upgrade one, upgrade both, or sell the one that doesn't get used any more.
Hint: Always keep both bikes clean and oiled because believe me, it's a bugger to come back to your geared bike after a year on the fixed gear and discover you'd put it away dirty (guess how I know this).