Both designs are parasitic, its just that a turbo is less parasitic, ie more efficient.

A properly sized turbo system (it takes more than just a turbo to make power) will not have any noticable lag, have a fairly flat torque curve, be reliable, AND make more power than a supercharger. Most people don't get a turbo sized to do that though, they get ones more for higher hp numbers which neglects on some of the other areas.

End story; turbos more efficient than superchargers. Go physics!