Consider the efficiency losses of a piston engine when you compare it to a turbine engine that spins on one axis creating uninterrupted power, with intake, compression, combustion and exhaust occurring simultaneously.
The airflow that is effortlessly flowing through the engine is simply injected with fuel which combusts, and expands imparting its energy to turbine blades which turn and drive the prop or reduction gearbox.
No components reversing direction, minimal frictional losses. So simple.
On a piston engine, the intake air has to be delivered to/through the cylinder head at specific points in time by going through intake and exhaust valves which are driven by a valve train, complete with the weight of two camshafts (per head) and the chains that drive them. All these valves are housed in a complex and heavy cylinder head.
On the current general aviation aircraft gasoline piston engines (which aren't much more advanced than an air-cooled horizontally-opposed flat 4 on a 1960 VW Beetle), the aluminum head will crack if it is shock-cooled during a descent with a low power setting.
However, the Thielert Diesel on a Diamond DA42 TwinStar is water-cooled, which avoids this problem... which reminds me that the cooling system on a jet uses the already abundantly available compressed air created by the engine's compressor section, while a piston engine that uses fluid for cooling needs to enclose the combustion chamber with coolant.
Yet more weight.
Once a piston engine finally meters its air and fuel into the combustion chamber it creates power from gas burning and expanding,
pushing pistons down into a cylinder, which are connected through connecting rods to a crankshaft that must be attached to an engine block strong enough to take all these loads.
Not only are these pistons reversing direction (which makes it possible to "throw a rod"), but the intake, compression, combustion and exhaust cycles occur sequentially, not simultaneously.
This is more wasted efficiency and frictional losses as the piston slides against the cylinder wall (creating no power on 3 of the 4 strokes) as it wears its piston rings away (all of which must be lubricated), as it charges towards the next mandatory engine tear-down and overhaul after only 2,000 hours of service, due to all of this friction wearing piston rings, cylinder walls, camshafts, valves, water pumps, etc...
All These parts that wear out on a piston engine and limit its lifetime, requiring a mandatory overhaul, don't even exist on a turbine engine.
I don't think we even need to compare performance numbers.
If you are going to fly a single-engine piston airplane over an ocean you better make sure your will is prepared because of piston-engine reliability thanks to all these different parts that could fail unexpectedly.
The failure of an oil pump or water pump, alone, will be the end of the engine.
If you are going to fly a single-engine turbine airplane over an ocean it's "just another day at work".
Reliability, maintenance and weight are a few of the reasons that piston-engines haven't been put on airliners or commuter planes for many decades.
Piston engines are early 1900s technology... and, compared to a turbine, they lack power above 5,000' altitude unless you add the weight of yet another costly piece of equipment- a turbocharger.
Nobody wants to fly on DC-6s anymore. Not even a diesel version. ;)