When we re-did our old driveway last year (original was 24 years old), we were quoted two prices. Now, in our case, it was already paved before, so the first price quoted was to remove all the existing asphalt, re-grade and compact it, and then re-pave it. The second price which was a several hundred dollars more expensive was to remove the old asphalt and fill down to 14 inches, put in 12 inches of crushed stone, grade, pack and pour new asphalt. We also got our driveway widened 4 feet on one side and about 3 feet on the other.
The company came in and slammed the bucket of their Bobcat down into the existing fill in three parts in the driveway (top, middle, bottom). In the top and middle, we found quite a few bricks and other debris. At the bottom we found another asphalt driveway that went up about 6 feet up from the bottom, that surprised everyone who was standing and watching that day. The fill was not clean, and we decided to have them remove everything and start fresh. That way, we knew exactly what was there. We ended up paying more, but in the end we got what we wanted. The true test will be in the spring and summer to see if there is any shifting of the driveway.
Best bet is to call around and get some quotes - we had seen the work of the paving company we chose and the price was pretty good, so we went with them.
Best of luck, whichever direction you choose.