Concrete is more expensive and much slower to build, but lasts longer than asphalt. Concrete is terrible to repair or rebuild (unless you overlay it with asphalt). Concrete is better in very hot climates under slow moving heavy aircraft because it doesn’t rut like asphalt. Concrete is better for very busy airports. IMHO where you see concrete, it is because the engineers have done all the sums and it came out best. And vice versa where you see asphalt.
While some type of textural finish can be constructed in a concrete pavement surface prior to grooving [i.e. brush or broom finish, heavy burlap drag finish, wire combed or wire tined construction], these texturing techniques cannot be substituted for saw cut or plastic cut grooves because they do not prevent aircraft from aquaplaning.
Grooves last longer in concrete than asphalt. They are much more stable. They don’t close-up like in asphalt, and rarely get damaged by the rubber removal methods. If you cut the grooves deeper at the start (say 8mm instead of 6mm), they can be very long lasting indeed.
I still prefer asphalt runways with maybe concrete runway ends. When things go wrong with asphalt, it generally can be fixed with overnight closures while the runway stays open 16-18 hours a day. But for a brand new mega-airport with say 6 runways and lots of redundancy and lots of money, concrete is often the better choice.