The concrete driveway costs between 30 and 50% more than asphalt. For that you get a permanent surface. Asphalt costs less and initially looks great. To keep it that way, you must seal it in the first year and every two years following. Asphalt will soften in hot weather. Objects that exert an extreme load (motorcycle kick stands, car parked on a stone, dumpster) can cause surface failures. I have even seen mushrooms grow through asphalt.
I personally used asphalt recently on a 5000 square foot project. The decision was based on budgetary concerns, and it looks great. If I could have done concrete, I would have. One thing is for certain. After living with a gravel drive for 9 years, the pavement was very welcome indeed. Snow clearing was a snap, the house was cleaner and the property looked great.