A supercharger extracts more useable energy from a smaller engine at the cost of greater fuel consumption, ie: greater power / weight ratio.
A supercharger compresses air flowing into the engine. Stuffing more air in means stuffing more fuel and only then have you boosted energy potential. If they could get away with leaning out the fuel with more air they would - but the range of fuel-air mixture porportions that will burn in useful & controlable manner are very narrow.
The higher density fuel charge is 6 + pounds per square inch over normal atmospheric pressure so 50-percent more air/fuel goes into the engine but up to 40% of that gets lost: parasitic friction load of the supercharger, exhaust valves opening before fuel/air charge completly spent, extra heat and vibration.
Turbochargers can impede gas flow at high rpms where superchargers are a constant load that can affect low rpm and allow better high rpm power, but turbochargers are thought as the more efficient method because it scavenges otherwise lost energy...
That answer your questions???