Superchargers pros:
easier to install
less heat
broader power band
less "lag"
no "surge of power" which can damage the motor and make driving more difficult
more reliable
easier to tune
doesnt restrict exhaust flow

Turbo pros:
more efficient
capable of more power
much quiter
doesnt draw power from the crank

I like both but I like superchargers(mainly centrifugal superchargers) better. However to say one is "better" is just an opinion!