Why would a turboprop be better than an internal combustion engine for a UAV?
Mostly reliability, and weight.  A TP is far more reliable than a piston engine, and much lighter.  The TP's lighter installed weight makes up some for its higher specific fuel consumption.
You would use a piston engine to get operating costs as low as possible, and you're willing to live with lower reliability (you're forced to use turbocharging or supercharging, which reduces reliability further), and one of the new turbo-diesels would be the best option in that case (close to half the fuel burn of a TP and able to run on kerosene, or diesel perhaps).