I've been in the concrete biz for 20 years and my brother in law's family owns one of the biggest asphalt plants in Kansas City. Before you start trying to determine the difference in the cost between the two, you need to decide how much you want to screw with it in the future. If concrete is poured the right way, the extra money you spend on the concrete driveway vs. asphalt will seem like a drop in the bucket when you start adding up all of the times you have to seal and maintain the asphalt if you live in this house for a long time. I agree with Raymond on most points, except I always use rebar on 24"-30" centers instead of wire mesh and make sure it is pulled up into the concrete. Some contractors will place the rebar or mesh on the ground before pouring, and never pull it up into the middle of the concrete where it belongs. It does no good leaving it on the ground below the concrete pour.
I would like to be getting the prices Raymond is getting as new construction prices around here are going for around $3.50 per sq. ft. I guess you also have to consider the length of the driveway. If you have a long driveway, it may be cost prohibitive to do the whole thing in concrete. If it is, do the area coming out of your garage with concrete and the remainder in asphalt.
The whole key to doing concrete the "right" way is not to let the contractor pour the concrete very wet. The wetter they pour it, the easier it is, but it takes all of the durability out of the concrete. If you have ever seen driveways with the top coming off and flaking, it is probably because it was poured to wet. No more than a six inch slump IMO.
Good Luck