Just thought I'd throw off the flow a bit and say that a supercharger that does not have a clutch, or some other un-linking method, will actually generate vacuum and sap power at certain moments. I can't remember when all this is, but I'm pretty positive it's at low RPM. So where a turbo is generating no additional boost at low RPM, a supercharger is actually robbing power.
The newer Mercedes kompressor cars have a clutch assembly in the supercharger to prevent this. It can actually disable the supercharger at times when it's not needed, helping both power and fuel mileage.