Ad: This forum contains affiliate links to products on Amazon and eBay. More information in Terms and rules
Turbo chargers are very good at several things one of the biggest is that a turbos can raise the apparent compression ratio which in turn makes more hp per lb of fuel. The difference between 9/1 and 10/1 compression is an increase in power and fuel efficiency of 10%. A turbo charger has more flexibility to provide additional boost that acts like added compression to the engine.
Mechanical superchargers are tied directly to the engine and provide "boost" based on the RPM of the engine/throttle opening. Turbos operate by using the heat expansion of the exhaust.
At cruise a Merlin as set up in a P-51 had a fuel consumption of .60lbs/hp/hr at 2000RPM and 27"MAP producing 500HP
A P-38 could by using 1600RPM and 31"MAP could produce 525HP at a fuel consumption of .46lbs/hp/hr.
The second thing Turbos are good at is a consistent power level an Allison rated at 1600HP at sea level can with a B-33 turbo maintain yhat power level to 25,000ft. A mechanical supercharger will have "steps" the power will be high then drop off as the air thins with altitude.
davparl -57 is a newest variant, i think is best compare a -21 with a -18