Really like turbos.
70% mechanical efficiency vs. 30% There's a good start. And power(and fuel slurping) when you want it, not all the time. And they sound really good on larger engines.
Supercharger. Power where you can actually use it more! And where it's better. Drags and things were you need power from a stop the supercharger is better.
A turbo is only really good at high RPMs [or higher speeds] so they generally only come into real use when your going faster than the speed limit anyway!
turbo less drag on the engine and easier to crank the boost up higher plus can have full boost lower in the rev range and can choose when to boost and how much just with accelerator pedal control
Turbos in the end a better more efficient invention, but a roots or whipple screw supercharger has advatages over the turbo for some kinds of competition. Centrifugal blowers combine the worst of both really, I'm not even sure why they exsist, I guess being easy to install is something