[TimT]

Asphalt is flexible pavement.

Concrete is rigid pavement...

With either, the most important thing you can do, is have a proper base to place the wearing surface on...

Given that this is a driveway that will see at most a few cars a day traffic, make sure the substrate, which is what the base is placed on "walks well" walk with hard heel strikes i.e where you feel soft spots areas with excessive fines, pumping usually means layers of clay that should be removed.... have the contractor dig out the offending areas little more $ and replace with a blend (recycled concrete is great)

Then a a few inches of blend, and either asphalt top, or concrete, you would be looking at a driveway that lasts a really long time...

Now if you want to add some subsurface drainage ;-)