My experience is varied.
We have 3 cars:
Morgan Plus 8: Natually aspirated. Runs more cleanly/smoothly, especially pickup at low RPM, and slightly better MPG on V Power. So used all the time.
Mercedes E350D: Turbo. Using Shell VPower diesel MPG improves, on a long run, best seen is 48 compared with 35 around town normally. Used V Power every 3rd fill-up or before a long run.
Mercedes CLC 180 Kompressor: Supercharger. No measurable difference, so the cheapest fuel available is used.