I faced this delimma last week, redo asphald driveway or go with concrete. Old asphalt was in terrible shape, previous pavers must have used rented equipment. Price for concrete is more than double the price for asphalt ($2 sqft asphalt/ $4.50 sqft concrete). I'm comfortable saying for most the preferred material is concrete. Just about everyone agrees on that (except for the one guy that had his concrete removed and replaced with asphalt because snow melter faster on asphalt...).
As almost always with the working class...it's a manner of economics...
Yep....I'm that guy
If I lived in a warmer climate, I would most definitely go with concrete. But my vehicles don't leak either

With asphalt at least you can cover it.
Don't take it wrong, I'm not trying to defend myself or sway one persom to go with asphalt over concrete, but in my situation, we had a concrete turn-a-round driveway directly across from a "T" road. Everyone thought it was just convenient to use it at their own convenience. Also, in the winter when we had periods of warming during the day and freezing at night, the way our house faces, the sun would hit the drive just enough to thaw it a little, then by noon, it would start freezing again. A few winters, we had to go as far as hooking the hose up and slowly running water underneath the ice so we could break it up. We'd have a couple of inches of ice. I have one good arm to chip away at it, and I don't want my wife out there doing something I should be doing.
So in my case, asphalt had it's benefits over concrete. When we had the turn-a-round drive, we just had a sidewalk put in from the front porch out. Three days later, some ****** decided to use the drive, drove through the yard, flowerbed, and ran over the sidewalk breaking it in half. I do not miss a turn-a-round whether it be concrete or asphalt.
I've tore up my asphalt drive though. One was from leaving my car trailer setting for a week. It was up in the upper 90's. I went to move it and the four tires left indentations along with the tongue jack. Another time, I had to look under my GMC Jimmy and took the floor jack out to raise it up. It was only on the jack for maybe 10 minutes but I have 4 wheel marks from it. When the time comes that I have to redo the driveway, I'll either make a concrete pad out farther or make a concrete pad beside the garage.
As far as longevity, if the OP is looking for something to last for years and years, by all means, go with concrete AS LONG as it's done correctly. I would never recommend the wire mesh to anyone for concrete. I would only go with rebar for the fact that IF or WHEN you get a crack, the rebar will let it crack but keep the two pieces from shifting up and down from one another. Also, the fiber reinforced concrete WILL NOT prevent it from ever cracking.
It take someone that really knows their business though work with concrete to keep cracks at a minimum, knows where to put control joints, and knows what to do to make it last for years to come. Most concrete today is not like concrete was 50 years ago or more. Back in those days, when concrete was poured, you knew it was going to last. In a small town not to far from where I lived, they had a concrete bridge that train tracks were on over the road. The tracks were abandoned and they were going to tear out both sides of the bridge and regrade the ground. What was going to be about a one week job turned into a full summer. Jackhammers would only chip away a little at a time. A wrecking ball would not hurt it except for a few scars. They ended up bringing in a big track-hoe and digging out behind it, hooked up some hose to the fire hydrant and undermined it to get it to drop into the hole. Now that was some good concrete. You just don't see that today.