I'll take a shot.
There are tradeoffs for both turbochargers and superchargers. Superchargers are mechanically driven by the engine to create boost. The benefit is for the most part they make their boost throughout the RPM range and instantaneously create that boost right along with throttle inputs, however because it's a mechanical linkage they also take a good amount of HP to run on the high-end to create that boost so it limits the overall output more than a turbocharger would.
Super chargers come in a couple different varieties, roots-type and centrifugal type. A roots type like a twin-screw is the most common, they sit right on top of the engine and suck in air directly. A centrifugal type is basically the business end of a turbo that is mechanically driven instead of exhaust driven. A roots type like what mn_vette said gives low-end boost and tends to run out of steam up top. A centrifugal type is like a turbo where it makes boost at high rpm, down low you experience mechanical instead of induction lag which makes centrifugal type superchargers feel similar to turbos
A turbo spins independently from the engine using exhaust to generate the boost. They tend to be much easier on an engine and give their numbers with far less sacrifice to fuel economy and reliability when compared to a supercharger. A turbo multiplies it's output with it's own output, the boost puts more air in the engine, the engine gives out more exhaust, the exhaust spins the turbocharger.
A supercharger doesn't have the benefit to take advantage of it's own output like that, it takes HP to run and somwhere along the curve the HP it takes the engine to spin it will outweigh the HP it creates causing a drop off on the top end for roots-type blowers, and mechanical lag down low for centrifugal type. However, because superchargers are mechanically linked the boost follows the engine instantly and throttle response is preserved.
Turbo's overall are a better and much more cost-effective way to achieve power numbers. However, a Supercharger will allow you to go more balls-out on power while sacrificing less throttle response at the expense of being expensive, much higher in maintenance and much harder on the engine.
There's a good section that summarizes all of this in this wiki article
http://en.wikipedia.org/wiki/Supercharger
All in all, I believe you can make higher HP with a supercharger which is why drag engines tend to use those instead of turbos. But for a track car, turbo's allow for more reliable output as a supercharger would eventually eat the engine in most cases.