My grandpa started a sand/gravel business and poured many concrete driveways and walkways. The company also has paved almost every stretch of highway (asphalt) in the region since the 40s, as it's the only gravel pit in the area.
If you live in a cold climate (like michigan) and chose concrete, don't go cheap, and reinforce it with rebar. The concrete in front of my parents house was poured in 1946 and although it's stained from 50 years of cars and worn from 50 years of spring frost heaving, it's got few cracks in it aside from the strip where a car litterally landed on it's side on it and left a line of broken concrete.
My landlord's driveway was done cheaply with concrete, 5 years ago, and has a crack every 6 feet. It's also shedding alot every spring. Withing a few years it will look like crap.
With Asphalt many spills like gasoline will eat into it, as stated it also needs re-tarring. Once in awhile I take out my garbage with my socks on, I wouldn't do that with asphalt
Asphalt is also affected more by frost heaving in the spring, so the driveway will possibly not remain level. This is easily remedied by not skimping on the gravel base of the driveway. Properly done the driveway should remain level year in year out. There are certain steps invloved in the layers beneath the asphalt, but alot of people ignore some of them to save a buck.
There is a driveway back home constructed of 1x1x3 blocks of the best concrete they mixed and each block is reinforced with rebar cages, it was laid out in the 60s and still looks new. The concrete wasn't very pourus so it doesn't seem to stain, and the blocks are indestructible. My parents house has some of the same blocks used as a retaining wall along the side of the driveway. If you are planning to live in the same place for a long time, blocks like that might be a nice option, although probably not cheap.
04 WRX - TOTALED 3-5-05
Previoius Owned: 96 Contour LX with svt kit