I can't think of any mass-production cars that use both a turbocharger
and a supercharger.

Turbochargers have the capability to generate a lot more boost and
ultimately make more power than superchargers.  It's also a lot easier
to fit an intercooler to a turbocharger or a centrifugal supercharger.

The drawback to turbos is that they take a moment to "spool up" when
you press the throttle, and if the engine doesn't have enough torque
on its own before the turbocharger spools up, you can get a pretty
noticeable lag.

If I were building a performance engine from the ground up, I'd make
it large enough that it had enough torque even without forced
induction, and then I'd also put a turbocharger on it for more power.

For smaller production engines, superchargers are nice because they
generate boost constantly, with no "lag" when you apply the throttle.