Of fucking course asphalt will look more damaged. If you try to use Roman roads for buses and trucks, they'll be destroyed completely within a couple of years (road damage scales as the fourth power of the axle weight). Cobblestone is also slippery when wet or iced.
Paving stones might look nice, but they can get dislodged, or the road can warp if drainage is not done properly.
Everything in engineering is a trade-off. You can use concrete for paving and for a small neighborhood road it'll last for decades with little maintenance. But it's much more cost-effective to use asphalt on a gravel bed, and just periodically do spot repairs.
As asphalt becomes more expensive with the winding down of fossil fuels, we'll switch to more concrete roads. But we sure as hell won't be using paving stones.