Typically, the argument is that a turbo makes more power than a supercharger, which is not entirely true. For instance, the Lysolm (aka "screw-type" Supercharger, known as the PSI in Top Fuel) was the choice of forced induction for Top Fuel cars for years until they were banned for giving an unfair advantage to the cars using it. If it's good enough for Top Fuel, it's good enough to make some pretty good power on a street car. Now, don't get me wrong. I'm not telling anyone to run out and buy themselves a supercharger right now. In fact, I'm not even implying that it's better than a turbo. I'm just making a case for it. Just as I'll make a case against the idea that turbos are all about lag and disproporational power curves. That's not entirely true. A turbo compressor that is well matched to the motor and tuned properly can result in a car that makes power smoothly over a broad powerband. Per a conversation with Texan, the Audi R8, a LeMans car running in the LMP900 class, is a good example of a turbo car that drives like a very powerful all motor car.
Admittingly, both Top Fuel cars and LeMans cars are not the best examples of your everyday street turbocharged/supercharged car, but it's to make a case that either device can be good IF the car is properly tuned with it. Most of the myths about turbochargers and superchargers