In general, concrete will last longer before needing to be resurfaced. I believe in road construction, asphalt roads need to be resurfaced usually every 5-10 years, while concrete only needs to be resurfaced/replaced every 15-20 years. There is more to the decision than just cost and longevity though as an asphalt road can be put down in less time, which can make a big difference in how long a road or other surface is unavailable.
As for airports, in the US there are plenty of examples of concrete runways and even all airport surfaces being concrete vs asphalt or a mixture.