A concrete driveway is generally more expensive because it requires more hand labor to install. An asphalt driveway is installed mostly with power equipment (spreaders, rollers, etc). Concrete requires excavation, forming, steel reinforcing, pumping, placement, finishing the surface, and, finally, curing.
A 6″ thick concrete driveway will be much stronger than 2″ of asphalt and will “span” over soft spots in the subgrade. If you have a steep driveway, concrete can be broom finished to give better tire traction but asphalt must be install “smooth” and can be slippery when wet. Concrete will obviously be whiter in color vs. black asphalt. “Lamp black” can be added to the concrete at the plant to make it more grey, so it doesn’t blind you in the sunlight.
So you might want to get a quote for both asphalt and concrete based on your current site conditions.
Folks need to remember that concrete needs to be “cured” for at least a week after placement by sealing it again water evaporation. Expansion joints also need to be installed, since concrete shrinks during curing and will crack randomly, if not provided with “control joints”.
Hope this helps.