Rob makes a good case for concrete, no ifs, ands, or buts.
But (ooops!) I have a preference for asphalt, at least in my particular situation. As Rob says, asphalt looks nice and is less expensive and requires more maintenance than concrete. Thing is, for me, a concrete driveway, unless it's for-the-most-part going in on predominately flat terrain, could be asking for trouble. Asphalt is a bit lighter than concrete, and concrete can 'slip' if it's on an angle where it will 'pull' down. This type of stress can crack the concrete or pull away at expansion joints, and in my opinion, it can be tougher to fix than if it was an asphalt 'patch' you needed to do. Also, after patching asphalt, you can coat it and seal it, along with the entire driveway and it will 'look' nice. I know you don't sleep, eat, and entertain your guests on your driveway but looks have their merit. A patched concrete crack or hole, well, it looks patched. But if you were to walk up to a house where you see a few patched concrete 'failures', you might begin to wonder if there are more to come.
I'm not knocking concrete. Like asphalt, depending on the terrain, and what the rest of your neighborhood has, and what 'looks good' with the house, and what maintenance you might have, the choice is not as easy as you might be led to believe otherwise. I'm only trying to 'stir' your brain. Now, one last thing. About having to coat an asphalt driveway on a regular basis is absolute non-sense, IMO. You should really only be recoating the asphalt when you see the 'white' of the stone. This means the asphalt on the top of the stone has worn off (or broken down) and is beginning to wear BETWEEN the stone. If this break-down process goes far enough, you'll have a cinder driveway! The elements AND the sun will evenly break down the asphalt. It's not just where the wheels of the car happen to ride all the time. And if you go with asphalt, may I suggest you wait a year or 2 (ask your contractor) after the asphalt is laid to 'seal' it. This way the driveway has a chance to settle and the weather has affected it for at least 4 seasons. When you do seal it, I suggest you use a sand-sealer. This reduces slipage and improves traction in both snow and rain. FYI, my neighbor sealed his driveway EVERY year for the 5 years I've known him, and guess what he's doing this summer? A contractor is ripping up his asphalt and relaying a new driveway! Why??? Because he said, for a fact, the reason he sealed his driveway every year is because it looked nice! NOT because it needed it. He put so much sealer down that on hot days, the car tires left tracks in the sealer AND it got tracked into the home. Like I said, you park your car(s) on it and it drips all kinds of junk on it so there's no need to keep it looking so nice EVERY YEAR. I've had my asphalt driveway for 4 years and I've only sealed it 2 summers ago. I'm not tracking anything but what's on the driveway (grass, fine gravel, etc., etc.). Not any sealer, and I don't envision having to seal it for some time to come.
This is a lot so I'm gonna quit. Best to ya and hope it makes your more informed. (Nice post Rob. It's a great sell. I'm sure Dave appreciates it all. :) ) Don't forget to 'look around'. Ask how folks, with similiar terrain, sun, and shade as you have faired with their concrete (or asphalt) driveway. Also remember that someday you may have to sell your home. If you're out-of-context with the rest of your neighborhood, you could bring the value of your home down going the 'opposite' way.