I like Kendall's cost comparison between the two systems. Bang for the buck, which is how Corvettes are normally compared to European Supercars. But, then again, if cost is no object, the situation may reverse itself.
I would rather compare the two systems with the idea of equality. For the same result, and that result being equal Rear Wheel Horsepower and Torque (RWHP & RWTQ), how do they compare?, since each can achieve identical levels with enough money, hardware and engineering. I see it as follows:
The supercharger system is likely a less expensive and more performance oriented system up to about 1,000 wheel horsepower. However, let's not forget that to achieve this level, the prime mover (the engine) must create enough power to operate the supercharger, in addition to the power to the transmission input shaft. At a given point (which I have postulated to be at ~1,000 rwhp, a debatable number), the strength of the motor should be increased to withstand the total power that the prime mover must generate. In contrast, the turbocharger system does not place much more strain on the prime mover - just the additional restriction on the exhaust cycle to spin the snails. Once the momentum has gotten the unit spinning, the turbo can increase boost without significant additional strain on the bottom end. So, while the supercharger system may be less costly up to a given power level, above that level will require significant cost increase to the strength of the prime mover due to the demands of the supercharger, whereas to reach that same level with the turbo system will allow the power to be transmitted more efficiently.
Thus, each sytem has its advantages, depending upon the desired rear wheel output level of the system.