Are turboprops more efficient than piston engines (thrust per fuel consumption)?
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.