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well that is a very very loaded question.
Here is the abbreviated version.
Supercharger(65-70% efficient power adder)=pain in the **** belts always slip or give you greif somehow. But there are kits readily available (flawed ones some would say) and it is the fastest way in the door with less initial cost.
Turbocharger(80-99% efficient power adder)- must be custom made. It has the ultimate in torque and horsepower with more or less power just a boost controller away. It is the most expensive and most complex route, however once done(if done correctly) there is no periodic maintenance other than the normal engine maintenence. Nothing wow's em like a turbo trust me.
Full boost comes on at a lower RPM and you don't loose boost when you shift. That was my big concern with a supercharger, when I shifted the boost would go from full to none and then build back up again.