I will try and give as HONEST of an answer as I can if we can specify a few parameters.
Lets say your F1R can make 1000 hp based on moving a given amount of air at the same 25 psi in the Intake Manifold.
You will never see that 1000 hp in real life (in this example) as the supercharger is belt driven and consumes a given
amount of HP that the engine is making.
It is a well known rule of thumb that it takes about 1 hp to move 1 lb of air.
A supercharger has other losses from the belt and from the mechanical parts in the supercharger so 15% added to
the "Air Power hp number.
Supercharger Flywheel hp would be:
100 lbs of air moved makes 1000 hp minus 100 hp to move the 100# of air plus 15 hp for the other losses =
1000hp - 115hp = 885hp at the flywheel (Given the right camshaft, same heads, right exhaust, right timing, etc)
Now we do the Turbocharger
Same rule of thumb of 1 hp to move 1 lb of air.
A Turbocharger has other losses (No belt or mechanical losses but it does have back pressure)
BUT WE DO HAVE EXHAUST ENERGY AND EXHAUST TEMPERATURE
Turbocharger Flywheel hp would be:
100 lbs of air moved makes 1000 hp minus about 15 hp for exhaust back pressure =
1000hp - 15hp = 985hp at the flywheel (Given the right camshaft, same heads, right exhaust, right timing, etc)
If we assume the common rule that 1/3 of the total energy goes through the mechanical parts, 1/3 goes out of
the exhaust, and 1/3 goes into the cooling system we can then assume that the exhaust contributed the 100 hp
that drove the Turbine wheel and therefore the compressor wheel to move that 100 lbs of air per minute.
IF you do not have the right camshaft, IF you do not have a proper Turbo Manifold system, IF you do not have the
right exhaust system after the Turbo, the numbers will change just like they would on a "Belt System" if you made
a mistake there.
A Turbo will make the same heat across the compressor side of the turbo moving the same amount of lbs of air but
there will be a very slight increase in temp from the center housing oil cooling and water cooling not being 100%
efficient. But the number is a small difference.
A Turbo will always make more power at the flywheel vs a "belt car" as the turbo is using (as was mentioned FREE
POWER from the exhaust).
About as honest as I can be.