The airplane had a huge turbo supercharger that, by a combination of drag and mechanical power bleed off must have caused a substantial performance degradation at other than optimum altitudes. I know a couple of people in a Bearcat squadron who had an inadvertant encounter with four late model P47s one day in 1947. ( Inadvertant, hell. The Bearcats jumped them. What did you expect. The P47s were there.) It was no contest- partly because the Bearcat, below 10000 feet, could do absolutely everything better than anything else with a propeller and at low altitudes could out accelerate most contemporary jets.
Kind of comparing Apples to Oranges here aren't we?
And I would like to know just what "mechanical power bleed off" you are referring to for the P-47.
That was the whole point of the turbo charger, use the power of the exhaust to run the supercharger rather than powering the the first stage of the supercharger using crankshaft power.
F8F also carried a bit less internal fuel than the P-47. One source giving 185 US gallons vs 370 gallons for most of the P-47Ds let alone the tankage in a "N". Cutting the guns from 8 to four didn't hurt and dropping over 50 sq ft of wing didn't hurt either.
Trying the combat at even 20,000-25,000 ft might have given rather different results also.
One reason the F8F was so small was that they "lost" the two stage mechanical supercharger of the F6F and F4U with its associated inter-cooler and were fitted with either a mechanical 2 speed drive on the F8F-1 or a variable speed hydraulic drive on the F8F-2 for the single stage supercharger.
While all the R-2800s in the P-47, F4U, and the F6F were rated at either 2000 or 2100hp for take-off (by the factory and without water injection) the altitudes at which they would maintain "military power" are rather informative.
The 2000hp engine of the P-47Ds was good for 2000hp military power to 25,000ft
The 2100hp engine of the P-47Ns was good for 2100hp military power to 28,500ft.
The 2000hp engine of the F6F and F4U was good for 1800hp at 15,500ft and 1650hp at 22,000ft.
Later F4U engines could do better
The 2100hp engine in the F8F-1s was good for 1700hp at 16,000ft.
The 2250hp engine in the F8F-2s was good for 1600hp at 22,000ft but the first F8F-2 with this engine wasn't delivered until 1947.
The Non-turbo engines will, of course, have some measure of exhaust thrust to add to their mechanical HP but their longer exhaust passages compared to the V-12 engines cuts that a bit and since exhaust thrust works better the higher you go it may not have been a really big difference below 10,000ft although helping to even things up at higher altitudes. Exhaust thrust is also highly speed dependentant so that while it helps a lot in a high speed dash it doesn't work so well for climb performance.
It is amazing what 2-3 years of aeronautical knowledge would buy you in the WW II era let alone what 3-5 years would buy in engine and supercharger design. The -30 engines used in the F8F-2s were almost identical to the -32 engines used in the F4U-5 Corsairs except for the deletion of the sidewinder 1st stage superchargers and the intercooler setup.