From past experience I prefer a supercharger for instant torque and performance. Turbochargers can produce extra horsepower from a little engine after they finally spin up while maintaining fuel economy. But what is the point of the extra power in a car when you have reduced torque from a little engine and you have to wait for the turbo to finally kick in... It is only about bragging rights for maximum Horse Power. Give me a supercharged V-8 any day.
Smoking tires is great.
Why not go with 4.10 or 4.11 gears in addition to supercharger?
BTW - SC will use more fuel than a turbo.
But this is all just flash and chin-wagging among braggarts, right?
You may find this 4 minute video interesting. It's from Jason Fenske on his YouTube page 'Engineering Explained', about twinchargers. He explains it very well. (He has quite a few other videos worth watching too).
https://www.youtube.com/watch?v=4birhPB5Twk
It involves bypass valves and a clutch on the supercharger. The supercharger handles the boost until the turbo spools up, they both run together through a crossover stage, until at higher rpms the clutch for the supercharger disengages and the turbo runs on its own.