What difference to the pilot does it make it say a runway is Concrete or Asphalt?
Does it require different information in the flight management system or other calculations?
Both are paved surfaces, so it doesn't make any difference when calculating takeoff and landing distances (ASDR, TORR, TODR, LDR). If your aircrafts performance computer offers the possibility to calculate the takeoff and landing performance, speeds and distances it won't make any difference between concrete and asphalt runways.
Also from the pilots perspective, not thinking about the calculations, it is not a real difference. Maybe asphalt runways are a little more prone to have standing water on it if they are not groved then concrete runways and also tend more to get cracks.
Airports will have their reasons why they decide for one of these types of runway. The condition of the surface the runway is build on (slopes, strength, water) as well as the costs will obviously be factors which needs to be considered.
Concrete is better for certain large airports. Asphalt never completely hardens, and will always behave like an extremely viscous liquid. So when you heat it up (on a hot summer's day), it becomes less viscous. When you put a heavy weight on it (like an airliner), it will tend to flow away from and surround that airliner. Planes pull up to a gate, sit for an hour or so, and suddenly their wheels have sank into the ramp six inches and they can't move. Same with runways, the constant shock of landing aircraft cause the asphalt to buckle and warp eventually.
Concrete has issues in the cold, however, especially if it is not laid well. It can buckle and crumble when it expands and contracts. However, it only gets stronger as it ages and it can easily be made to withstand the hardest of landing impacts.
The type of material does not make any noticeable difference to takeoff/landing performance.