They're more efficient in the air. Particularly at moderate speeds. Hard to spot an insurgent when wizzing past at 600mph, and then immediately turning around and going for a refuel. Being able to loiter in an area for a while, and getting a really good look around, that's more important when trying to find a target that would rather not be found.
That is a significant advantage over jets, but the US already has an ever-growing fleet of UAVs that can fill that role. UAVs are also smaller, quieter, and less likely to be spotted by enemies on the ground than a manned aircraft. UAVs even have the ability to carry out airstrikes too.
That's why the US looking to acquire a turboprop for counter-insurgency seems odd to me. Makes sense for nations that may not have the money to invest in UAVs, but not so much for a nation like the US that isn't afraid to throw as much money as necessary at the military. The only advantage a turboprop would have over a UAV that I can think of is what Broken_Erika already mentioned: Turboprop aircraft can take much more ground fire than a UAV and still stay in the air. UAVs are pretty fragile in that regard. I guess turboprops would be better armed as well with a UAV only carrying a few missiles, while a turboprop could be outfitted with an array of guns, rockets, bombs, and missiles.