Super charger and turbocharger are more useful in large engine especially diesel ones. As the diesel engine depends on lean mixtures combustion the decrease in specific fuel consumption will be obvious in these engines.
Supercharger used to increase the air flow rate into the combustion chamber which means higher air mass in front it needs higher fuel mass flow rate to preserve constant equivalence ratio. However, the fuel saving strategies depends on load and speed. In general, using supercharging will reduce fuel consumption for a limit.
In addition to what Miqdam mentioned above the supercharger itself needs power to rotate which is derived from the engine and so more fuel consumption is expected unlike a turbocharger. Supercharging enhance power output but at the expense of more fuel consumption.
Supercharging reduces specific fuel consumption of diesel engines (unfortunately in a small amount) for two reasons 1) energy of exhausted gases can be partially recovered 2) higher pressure inside cylinder improves fuel injection
Sorry, I did not distinguish between supercharging and turbocharging. The first, obsolete, would assume a mechanically-driven compressor. In this case, as Kamal noted, power to drive compressor can be only partially got from exhausted gases.
Guido if the compressor is driven by power derived from the exhaust gases then the only way is through a turbine which should be coupled to the compressor via a shaft and this arrangement is called a turbocharger not a supercharger. A supercharger is simply a blower that is driven mechanically from the engine.
Dear Kamal, I just forgot this, and remembered after writing. I had in charge Capetti collection of aircraft engines (Politecnico di Torino) from beginning to WWII. It has several supercharged engines and perhaps just one which is turbocharged.
Super charger and turbocharger are more useful in large engine especially diesel ones. As the diesel engine depends on lean mixtures combustion the decrease in specific fuel consumption will be obvious in these engines.