Boost is boost- it's become a cliché- but you can take it to the bank. So given the same engine @12 psi boost* whether produced by a SC or a TC will for the most part deliver the similar peak HP on that engine. (*increasing charge air temp differences are generally offset by the increasing HP required to spin the supercharger)
Uhhhhh, might want to take a step back and review your post. It seems that you made a slight oversight, one of which I am sure you were aware (from the other parts of your post), but simply missed;
The engine will indeed produce similar GROSS horsepower/torque numbers if the boost is the same, that much is true, however the boost from a turbo comes at the cost of some additional back pressure. Not that big of a deal. A supercharger gets its input from the crank of the engine. That is a big deal. At a guess, I would say the s/c takes at least 40 horses at full boost to spin it.
So, (assuming my estimate of 40 horses is correct, and it probably is at least that much) that means that the blower is sapping that much power off the crank and the NET output of the engine will be correspondingly lower. There is not that much heat difference between compressed air from a turbo and a s/c. Especially after running through a cooler. Certainly no where near as much temp difference to account for the power needed to drive a s/c.
So, pound for pound of boost, a turbo is more efficient at putting more power into the transmission.