Having the luxury of driving two almost identical engines, one turbo'd and the other supercharged, I can reliably report that the turbo engine has by far the greater performance and potential for releasing yet more power.
The s'charged engine is by no means a slouch but it readily loses ground to the turbo'd unit.
The supercharger engine makes for effortless driving providing respectable additional low down torque. Yes low down extra power delivery is immediate. In a sense this allows drivers who are unable to keep an engine reving and on boost or perhaps don't like to constantly rev an engine to exploit more power. The s'charger therefore is delivering extra power in a very different way and for a different purpose.
Driving a 2 litre supercharged engine feels very much like driving a 3 litre engine as progress can be relaxed and stress free. This is where it scores over a turbo but then this is where the advantage ends.
At higher revs the turbo can create alot more boost and hence power. Turbo design can determine lag and boost characteristics using smaller, bigger or sequential units.
I am not an engine designer so my understanding is only that of an enthusiastic layman but I can still appreciate basic engineering concepts such as turbo and super charging.
If as Tom argues there is indeed little to choose from between turbo and s'charged methods of forced induction why have the majority of manufacturers and serious engine tuners chosen to turbocharge rather than supercharge? Have they been toiling under a misunderstanding? I don't think so.
Real answer: Because turbocharging saps far less power from an engine and in return can deliver alot more 'bang' for your buck so to speak.
For small engines turbos make alot more sense. For larger engines s'chargers are employed to boost low down torque.
Turbos are also alot easier to incorporate into an engine. The revolutions that a turbo can achieve are far greater than a s'charger which is governed more or less by the speed of the crank pulley. They are belt driven which will also limit their revolution speed despite having a specific pulley gearing to increase spin speed.
At idle the supercharger is not producing positive but negative boost. Mine produces around -0.8 bar at idle and only becomes positive at about 2,500 rpm. Max boost is about 1.2 bar if I ever tested this generally planting the throttle in the Wilton produces about 0.8 - 1.0 bar boost.
In comparison the turbo spins according to the speed of exhaust gases leaving the cylinder head. Thus it can create a lot more boost when the gas flow is high.
Perhaps s'charger technology is set to make a huge leap forward. For the technology to catch up with turbos it would have to be an enormous leap. Great if it can be done, but some how I don't see it. I think s'charging will remain secondary to turbos on engine designers' drawing boards.
Andy