Forget driving style and all other varying factors. This is a simple math question. The more efficient the engine, the more power it produces from one gallon of gasoline. The more power it generates, the further it will move the car (under ideal driving conditions).
In general, a turbocharger captures wasted exhaust energy that is normally lost to the atmosphere, and makes the engine more thermally efficient. A supercharger creates more power by creating extra parasitic drag on the motor. Although it is possible that at certain RPM's and under a certain load (both sustained) a supercharged motor will have a higher peak of efficiency than a similar NA or turbocharged engine will, it is overall unlikely. A turbocharged engine is generally more efficient across the entire RPM spectrum. So with a standard "transmission", the turbocharged motor of equal design will generally create more power from every gallon of gasoline.
This is all general. There are many factors of course, like the terrain, the weight of the car, the transmission, the load, etc. Efficiency is not the same all the time. There are peaks and dips. If you create a situation where the peak can be maintained on one design, it will outdo the other two designs. In other words a supercharged 3.2 liter at 2750 RPM's carrying a certain load (weight, gearing, terrain, etc.) may be more efficient than the same engine with a certain turbocharger with the same load. Same with NA. Each design type will peak at a certain point, and each peak will be different. But driving inherently means you will not be able to maintain the peak for very long at all.
So the answer is not simple. It depends on the load, the tune and the transmission (even if driving style is mathematically perfect)... but to make it simple, I would just summarize and say yes to the turbo under most conditions, and no to the supercharger... this is simply based on what they are using as a source of energy.
By the way an electric motor blows all of these out of the water. It is generally close to 30% more efficient than all ICE (internal combustion engine) designs. The problem has never been one of efficiency but one of storage. A gallon of gasoline packs a lot of energy, much more so than 6 pounds worth of battery. If the battery issue is solved, looking strictly at numbers, ICE's (including the more efficient Diesels) are archaic.