I don't think either of those assumptions is quite right. Why wouldn't asphalt affect your tax assesment, if concrete does?
Things to consider:
Concrete is rigid, and won't flex if the ground moves. Concrete will crack. So the prep needs to be really good for a concrete driveway. In snowy areas, concrete driveways don't work well, because ground frost cracks them, and plow trucks rip them up.
Asphalt is super expensive now, due to high oil prices. So I don't know how they compare now.