This is just based on theory, but I think actual tests would agree...
Since a turbo-charger is propelled by the already present exhaust gases and the supercharger is propelled by the engine thru the use of a belt, the turbocharger will be "more efficient" and SHOULD result in better gas mileage than the supercharger.
Now as far as "same boost, same HP"...If you had the same boost on a turbo, you SHOULD see a good bit higher HP than the supercharger. Superchargers benefit from not having the "lag" that you may experience with a turbo since they are driven by the engine and produce power from the get go. A turbo "spools up" and generally will end up producing greater power in the long run, especially if you are talking about having the same boost.
Anyway, just my two cents and theory.