Turbos take power to run too

 

Of course, but the upside is that the power they are using is generally 'free' power in terms of it just being wasted energy otherwise. Typically that flow of hot gasses would just be exiting the tailpipe without use. A supercharger is always consuming some amount of energy to spin as it is connected directly to the crankshaft for its source of power (with the exception being the systems with a clutched pulley during idle/ low engine loads).

Certainly you could make the argument that an engine would make a little more power if something else were driving its turbo (ie exhaust from another engine) and as such that is the true horsepower loss of running a turbo via exhaust flow restriction. But the point is that a supercharger will never make the power of a turbo in part because they are mechanically drawing power from the crankshaft at all times just like any accessory (alternator, power steering, etc).
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