For what? If I am trying to hide a dead body, I would definitely go with Concrete, because it is much harder to break open when the exhume the dead guy.
If you are talking about driveways—we need more information. Where do you live? What are the temperature extremes where you are? Asphalt gets soft and makes ruts if exposed to too much heat. On the other hand, asphalt, because it is pliable, handles winter freezes better.
Concrete is very good in high heat, but it gets brittle and can crack because of earth movement in cold or humid areas.
Give us more information.