Here's a quick rundown on the pros/cons of a roots or cent. supercharger vs a turbo:
A roots type is great for low rpm boost, but lack the power up top. They aren't the most efficient means of compressing air, so as the boost increases it tends to heat the air considerably more than a centrifugal or turbo would.
A centrifugal blower does not create boost until higher in the rpm range. Max boost will happen at max rpm. Boost is dependent on engine speed. This happens because the compressor wheel is spun by a pulley off the belt.
A turbocharger creates boost by using the spent exhaust gases to spin a turbine wheel attached to the compressor wheel, thereby spinning the compressor wheel. The boost is not dependent on engine speed, but rather on load. Full boost will come in at a much lower rpm than a centrifugal style blower, and it will hold that boost until redline, unlike a centrifugal blower.
I personally prefer a turbo, but they all have their pros and cons. A roots has great low end torque, but lacks top end power. The centrifugal has great top end power, but the boost at low rpm is non existant and the boost curve is linear to engine speed. A PROPERLY SIZED turbo has good low end response and will hold max boost all the way to redline. A turbo will usually be harder to install and will create more heat in the engine bay. A centrifugal blower or a roots type are probably the easiest to install and don't create much more heat in the engine bay. The cost(at least for mustangs) is generally highest for a turbo kit (less availability and more complexity) then for either of the supercharger kits, but all things equal, the turbo will usually produce more power under the curve and make a more driveable car.