Are turboprops more efficient than piston engines (thrust per fuel consumption)? I want to compare two types of engines: Turboprops and piston engines. I want to know which one is more efficient. There are many types of efficiencies, so I will specify: thrust (in newtons) per fuel consumption (kg/second).

Right now I don't care about power/weight ratio or max speed or horsepower. Those are all valid concerns for aircraft design, but I'm trying to pick exactly one criteria and figure which engine is more efficient in its terms and its terms alone. I don't want to mix criteria. I want to focus on one aspect, get an answer to it, then move on to the others later.

A complication is that piston engines usually give their output in horsepower. I have no idea why this is. What's ultimately needed is thrust. I realize that a propeller engine's job is to create torque, and thrust will depend on blade length and airspeed. In that case, I can't understand why those engines don't specify their output in torque.

Citing engines that actually exist (and citing their specs) will answer this question as long as the choices are modern, good engines.

(I did not include turbojets or turbofans for fear of being too broad. I picked two propeller engines and don't want to mix them with jet engines.)

One more thing. I realize that engines are capable of varying levels of thrust. It's my understanding that max thrust is usually more inefficient than cruising thrust. Therefore, I will ask for thrust/fuel-consumption figures of an engine at typical cruise conditions.
No, piston engines are more efficient.

Their output is given in kilowatts or HP because this does not change much with speed, unlike the thrust of a propeller. By running a piston engine a few times on a dynamometer stand you can get reasonable numbers which are valid over the full operating range. If you want to characterize them by their thrust, you would need to look at an engine-propeller combination at one particular speed, which is not very helpful.

Now you ask for specs of contemporary engines. The funny thing is that the efficiency of aviation piston engines has not changed much over the last decades. If you assume 250 g of fuel per kWh at full power for gasoline engines, this figure holds already for good WW II-era engines like the Jumo 213 A which was run on 87 octane gasoline. The low octane number restricted compression to 6.93:1, while the higher octane number of contemporary AVGAS allows for an 8.5:1 compression ratio in engines like the Lycoming O-360, which consumes 280 g of fuel per kWh. Adding fuel injection enabled Lycoming to reduce fuel burn to 240 g per kWh in the IO-390, which was first run in 2002.

Diesel engines are even more efficient; they typically consume 220 g per kWh. This low value was already possible with the venerable Jumo 205 of the 1930s which consumed only 213 g per kWh at its most efficient speed. Modern aerodiesels run at similar efficiency: The Thielert range of engines which have been taken over by Continental consume 220 g per kWh.

Even the best turboprops rarely achieve less than 300 g per kWh. The most modern version of the venerable Pratt&amp;Whitney PT6 consumes 308 g per kWh, and only very recent developments can close the gap to piston engines. The Progress D27 claims a specific fuel consumption of 231 g per kWh while the Europrop TP400 one of 237 g per kWh. Note that here the remaining thrust from the exhaust has been converted into an equivalent power rating to achieve such good values.