On track you need progressive, predicatble response, so N/A is great. Anything that causes boost in performance will unsettle balance of a car which is important when most of the time the steering wheels are turned.
On a road car, I like forced induction. I point and squirt on straights. FI gives me a kick and surge that I like.
It will be supercharged OR turbocharged I believe - not both.
As suggested the VW twin-charged units do indeed have both.
Forced induction is important now. Emissions of a smaller engine during the standard cycles required for fuel consumption tests (and therefore driving CO2 outputs). That makes cars attractive in markets taxed on CO2 output, and makes cars attractive in markets where environment pressure is signifcant.
However FI gives the performance of a much bigger engine. Supercharging in particular gives the feel of a larger capacity N/A engine, and suits cars requiring a more sedate level of performance. Turbocharging (unless LPT) gives a different feel as it's less linear, making it more appopriate for cars requiring a sporty feel.
The driver for the use of superchargers in the 32/55K engines was down to three valve technology. An oomph was required as three valve engines generally don't rev. It suited the big engine hot rod feel that traditionally came with AMGs.
The market moves on. M-Power sell in greater numbers than Quattro and AMG, and both Audi and MB need volumes to be able to compete at an attractive price point. Influence of motoring press fuels the M-Power feel, and so Audi and MB moved in that direction.
The market moves on again driven by environmentally issues, and FI comes back into favour, and even M-Power use FI (eg X6, others follow).