both have advatages , yes supercharger is allwas working but doesnt normally give a higher bhp at max.
If u look at the super charger on the astin martin that needs somet like 150bhp just to work the supercharger, but will give more back in return
Or i think the new bmw has 2 turbos 1 small that kicks in at low revs , and then switchs to a big turbo at higher revs. theres also some sill low litre 1.* thats going down this route as welll