I've participated in these discussions about a billion times ( ), but I'll throw in the abridged version of my opinion on the matter:

Turbos are the better power adder because they operate much more efficiently, are capable of making more overall power, and can be quite versatile depending on application.

Which one would I put on my car? A supercharger. I've driven enough turbo cars to know that its hesitant power delivery can put a serious damper on autocross(the main purpose of my car). On a drag car, roadracing car, or street car, the answer would be turbo. No doubt.

There ya go