Turbo vs supercharger?

This is not a simple question. There are positive displacement (Roots style) superchargers, and there are centrifugal superchargers (Procharger, Paxton, Vortech) which apply boost more like a turbocharger.
The Roots style blowers can provide boost at very low rpm, and the added low end torque can make them a lot of fun on a street car. If the goal is a stoplight to stoplight runner, a Roots blower is fun and impressive to look at and listen to. The boost is immediate, basically from idle on up. There are several disadvantages to this style of supercharger, it consumes horsepower to drive it, it generally (but not always) requires hood modifications, and it heats the intake charge reducing charge density. On the other hand, it always increases power by a lot more than it takes to drive it, and there are intercoolers available for some of the designs. Plus they look cool, and the sound of a 3" toothed blower drive is badass.

For a more serious application that is occasionally raced, and where consistency is important, a centrifugal supercharger or turbocharger is generally preferred. These build boost more gradually as engine rpm increases, making the car less likely to lose traction right at the hit. You can also control the amount of boost with adjustable waste gate valves that open when a predetermined amount of boost is reached. These valves can also be used to control the rate of boost, or be timed to allow full boost at a specific time when going down the track. (Sort of like stacked nitrous kits) The tuneability of these systems are why they are so popular on big power (3500hp) pro-mod style cars. They are both more maintenance intensive, and generally require a lot more plumbing and an inter-cooler for best results.

For a street only car, I and many others prefer the "instant" torque of a roots style supercharger. They are just more fun in daily driving, as you don't need high rpm to make boost or light the tires.
However, if I was going bracket racing I would absolutely use a centrifugal supercharger, or even more likely a turbocharger.