in general, turbochargers more efficiently produce extra power, since they don't have parasitic loss as a result of a drive belt as superchargers do. They produce power from exhaust gases, in essence, meaning they are recovering and using free wasted energy.
However, this is a rather broad question you've just asked. The answer depends on what sort of driving you do.
For instance, a turbo would be best suited for WOT applications like drag racing, and high-rpm driving such as on a road-course. However, you might find it a bit laggy when autocrossing (although, proper turbo selection and setup goes along way in reducing that). For that, the instant-on boost of a roots style supercharger may be better suited.
Your overall power goals make a difference also, in terms of driveability.