I've always commuted on Mountain Bikes, and I'd recommend slicks. A lock out front fork is good as well- it means you can turn the front suspension off and use it as a rigid fork, although you do still have the extra weight of a fork.

1) Speed - how much faster and on what terrain?
A road bike will always be faster than a moutain bike on the road, it's what they're designed for. It's far, far more common for a road bike to pass me than the other way around. You can take shortcuts on a mountain bike you wouldn't do on a road bike.
2) Price
A mountain bike is better here. Compare say a Fuji Newest 2.0, and a Fuji Tahoe Comp. They're both within $50 of each other, but the MTB has better components, disk brakes and a front fork.

3) Comfort & carrying capacity

I've never ridden a road bike, so I can't compare it.

4) Flexibility - is it worth the whole new road bike if you just use it for commuting, or is a mtn/hybrid the best bang for your buck?

I bought a MTB instead of a road bike because of the flexibility it offered me. None of my friends have road bikes, so with a MTB I can go riding anywhere with them. Swapping the tires and locking the fork out can turn a go anywhere bike to a good commuter bike.

I'm still saving up for a road bike though. I figure if I save the money I'd spend on train fares in a year I can get a very nice road bike.