Is super charge faster than turbo charge?
Roots or screw supercharger... spooling Abosultely YES.
centrifugal like paxton,vortech, procharger, rotex it "spooling" depends...
A supercharger is directly driven from the engine, and therefore delivers boost all the way through the rev range(roots or screw supercharger), improving bottom-end response, Centrifugal can give more boost in first gear than a turbo in first gear from a stop) at the expense of losing a few horsepower because of the load on the engine of the supercharger.
A turbocharger uses exhaust gasses to spin up a turbine, which then drives an impeller, to compress incoming air, thus increasing horsepower. However, turbochargers are not very responsive at low RPMs, "taking sometime" to 'spin up', (really depends on the size of the turbo/turboes) this delay in speed, causes so-called 'turbo lag', where there is a delay getting the boost from the time you floor it, until u get boost.
So, a supercharger may make a car 'quicker' from an idle start, because of its continuous boost(roots/screw supercharger), a turbocharger is better when it 'catches up' because it doesn't rob as much horsepower from the engine.