I personally like asphalt over concrete for driveways.
One of my clients works as the office manager for the asphalt plant here in Tyler and they are constantly being sued. From what she told me, their are a lot of ways to cut corners when they mix up a batch of asphalt, and if you do not specify what you want with your contractor, they can save a lot of money on material going with lesser materials. You absolutely have to make sure that you get the same mix that the city and county uses for their roads. Terminology differs, and I would never trust a paving company to be honest with me on what that is. If I ever pave my driveway, I'm going to go to the plant personally and find out what the mix is used by the city. Then I am going to make sure to see the tickets issued to the paving company showing that is what they are using.
As for the base, if they add or remove any materials, in order to get it compacted, they will have to have a water truck there along with the roller. Right after I got out of the Marines, my first job was driving a water truck in CA for a large variety of construction sites. Getting soil and rock compacted takes a lot of effort and it has to be done in layers with the right amount of water. The size of the roller will decide in how thick of a layer you can go. Then before pavement was laid, the inspector would test the base for compaction. If we didn't get it, they tore it all apart, down to virgin soil, and did it again. Too much water is worse then not enough, but not enough water will also cause failure.
If they are doing all of that, then your price sounds very reasonable.