Turbochargers are great for high-end power and a peaky torque curve due the the lag since the turbo needs to spool up. Because of that, the bigger the turbo, the longer the lag and the less torque you have off the line. However, the potential for overall performance and power are much higher than a supercharger due to the ability to boost 1 bar and much further beyond (1 bar = 14.5 psi).
Superchargers (except for the vortex) are belt driven and work off the pulleys in your car. Since they are mechanical, they are limited by the size of the pulleys and the engine's baseline power. Because of this they are generally limited to 10psi and below in many import applications. However, since they are motor driven, the torque is instand and provides a long linear torque curve with great power off the line for very quick launches. The downside is the potential for higher boost pressure is bleak.
Many people in the import world prefer turbocharging to supercharging due to the higher potential for power in a small package. Also, turbo lag can be counteracted by simply using a nitrous kit that triggers at wide open throttle.