Let us consider a UAV, long endurance high altitude (~26,000ft). Why would a user (most probably military) go for a turboprop rather than an internal combustion engine?
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).
Reciprocating engines are somewhat more efficient, but they don't scale up well. A larger piston engine can't have as large RPM, but that means weight grows much faster than power. That's not a problem for ships, where huge diesel engines are common, but it is a big problem for aircraft.
On the other hand, turbines are very light for power even when large, and the larger ones are even more efficient.
That's why nobody even makes aircraft piston engines with more than about 170 kW. The higher power range is served exclusively with turbines. The common ones start around 400 kW and go well into megawatt range (largest turboprop, Kuznetsov NK-12, produces 11 MW and the turboshaft variants derived from large turbofans go up to the 40–50 MW range).
Additionally, turbines are significantly more reliable and require less maintenance. In piston engines, the pistons, but also valves are subject to huge linear accelerations, which causes a lot of vibrations and wear, plus there are many additional rotating components linking it all together. In addition to at least one turbine-compressor pair, because a piston engine to operate up at 26,000 ft will have to be turbocharged, otherwise the thrust-to-weight ratio would be way too low.
In contrast a turbine had just a turbine-compressor pair and a turbine driving the propeller, everything just smoothly rotating even though at huge angular speeds (in the PT6 the core goes up to about 45,000 rpm and the power turbine to about 30,000 rpm) with much less wear and vibrations. That means fewer inspections and overhauls, and fewer parts to stock and replace and that saves a lot of money.
Because of the air pressure at 26000ft the IC engine would have very little power without forced induction (turbocharger/supercharger) you then need boost control at lower altitudes to stop the engine exploding from cylinder pressure. You can't use a carburettor because you would get carb icing too, so it necessitates fuel injection. All these things make control far more complex.
The other thing is the vibration of a piston engine, this could affect camera focus or other unknown instruments.