Well, there's a large variation in what constitutes an 'asphalt' road -hot mix, warm mix, etc - but I think what you want to discuss is the difference between PCC and ACC - namely portland cement concrete and asphalt cement concrete.
But as was mentioned, location, weather, traffic patterns, etc all play a role in the 'lifespan' of a type of road covering.
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Most municipalities choose ACC over PCC because it has a lower initial cost to their budget.