It is certainly true that not all leaks have the same effect on power output.
A leaky inlet valve will cause blowback of mixture (during the compression stroke) and burnt gasses (during the power stroke) into the inlet manifold.
Both of these effects will reduce the amount of fresh mixture that is available for combustion. This will clearly reduce the pressure in the cylinders during the power stroke, which will reduce the power output.
A leaky exhaust valve will cause unburnt mixture to leak away into the exhaust manifold during the compression stroke. It will also cause exhaust gas to flow into the cylinder during the inlet stroke. Both of these factors will reduce the amount of fuel that is available for combustion. This in turn will reduce pressure in the cylinders during the power stroke, which will reduce the power output.
Leaky piston rings will cause the crank case to become pressurised. This increased crank case pressure will tend to reduce the amount of gas that is able to leak past the leaky piston rings. Most crank cases are vented into the inlet manifold, so much of the lost gas will find its way back into the cylinders (albeit mixed with a good deal of oil). This in turn will tend to reduce the amount of power that is lost due to the leaky piston rings.
So although leaky piston riings will cause less of a pressure loss than will leaky valves, the overall effect of leaks, wherever they are, is likely to be reduced power output.
The magnitude of this power loss will be determined by the size of the leak and its location.
For most practical purposes, if you anyone tells you that their worn out old engine is producing the same power that it did when it was new, then they are probably trying to sell you a dodgy old car.
Don't buy it.