For the past few years, I have commuted on a road bike for most of the year and on a mountain bike for late fall through early spring. My commute also involves both classic road-riding and more urban-style riding.
What I've Found
I've found that I prefer the road bike by a significant degree. Living in a hilly area, it is always a pleasure to drop the excess weight of the shock system, the efficiency loss due to bouncing and flexing, and the wide tired of my mountain bike come spring.
I can finally take my backpack off and put on panniers, which keeps my back from getting as sweaty and is generally more comfortable. My fenders work better to keep the mud off me. It is an altogether more enjoyable experience.
If I could ride my road bike in the winter, I would. Hard to do in the snow, unfortunately, especially when it comes to the turning bit.
What I Lose
However, when I switch to the road bike, I feel I lose some peace of mind. On my road bike, whenever I see a patch of sand at a corner I've got to take, whenever I ride in the rain over fallen leaves, I worry that I will lose traction and fall.
Furthermore, I've been run off the road before and gotten close to it several times and I feel much safer and more comfortable on my mountain bike knowing I can ditch the road and jump into the rough easily if necessary.
On my mountain bike, I don't fear to hop up or down the curb to, for example, avoid a runner in traffic. I can take shortcuts over uneven terrain, hop a few stairs, and be on my way.
Conclusion
In conclusion, I recommend finding a bike that fits your specific needs. If you can only have one bike, find the bike that allows you to do everything. If you live somewhere that gets significant snow, if you live in a place with terrible roads and worse drivers, you may need that mountain bike. If you live in a city with as many shortcuts and stairs as potholes, you'll love the "Go Anywhere" ability. If you live in a very hilly environment, you'll love the climbing gear on your MB. If you have any interest in actually mountain biking, keep in mind that a mountain bike can do both while a road bike has to stay out of the trails.
If you live in a more suburban area, or somewhere as flat as Kansas or The Netherlands, or if you live somewhere with nice weather year round, a road bike is the way to go. The ride quality will be higher; you will feel light as a feather, fast as a Ferrari, and much more efficient than on your MB.
TL;DR:
- Mountain Bike: true go-anywhere ability, safety advantage
- Road Bike: better riding experience, faster, more efficient.