Nope, just gearing, same frictional losses occur, when you change the diff ratio in a race car to suit a particular track that's all your doing, making it suit a condition better, you will be faster with the right diff but you still have the same Hp, your just utilising it better.
Maybe the questions should be,
How much more power does it 'feel' like I have with different geared diffs.
Throwing 31's from 33's on my bad girl feels like a 10rwkw increase.
Also to throw a spanner in the works how come everyone feels the need then to include tire size when they put up a dyno graph if they make no difference?
I for one thought gearing and tires affected output figures, well on paper anyway!?
All other things being equal (ie same size tyres) at the same engine speed you'd net a 12% increase in torque at the wheels.
Power is just the product of speed and torque and in the case of a ratio change it's a self balancing equation so at the same engine speed your 12% increase in torque is offset by a 12% reduction in wheel speed...net effect no change in power at the wheels.
But if you take a measurement at the same wheel speed for both ratios (ie 100kph) you will see an increase in power at the wheels as you've increased your effective torque and your engine speed - this is the gain you can feel on the "ass" dyno. The cost is shorter gearing.
Tyre sizes, tread patterns and wheel types all have a bearing on power output, compared to a std off the showroom floor vehicle. Changing diff ratios, as said above, allows the torque to happen at an earlier speed with more of it, but still the same revs though.