A big benifit to a turbo is that you hit full boost when it spools up and hold that untill redline. In many applications, you get a brief spike when it spools up which gives you a nice kick in the ass. With my Evo , it spikes around 23psi at 3500rpm and holds 20psi untill redline. The downside here is that untill the turbo spools, your diving with a low compression engine with a clogged exhuast. As long as you keep it on boost, all is fine. Fall off boost, though, and the car is a dog. This can make daily driving, especially in traffic, a pain in the ass, especially with a large turbo. If you look at the dyno charts of large tubo cars, like 1000hp Supras, the turbo may not spool up untill 5-6,000rpm. Great for the track, totally unstreetable, though.
With a supercharger, boost builds with engine speed, so you dont reach max psi untill redline. Benifit is that you're never off-boost, so you retain low end power. Day to day driving in traffic and what not is easier.