Differen't horses for different courses, as they say.
I have some interesting exerpts of Grumman test-pilot Corky Meyer's first flights in a P-47B. His basic assesment is that down low the F6F would out turn, out climb and out accelerate the P-47 and had a significantly lower stall thanks to its much lower wing loading, but that the situation reversed as altitude increased. In addition, the P-47 could leave the F6F behind in straight line speed, dive acceleration and rate of roll at all altitudes.
He noted that the Best climb speed of the P-47 was some 45mph higher than the Hellcats. and it showed a real reluctance to get off the deck. He found the stall speed was some 20mph higher than the Hellcat's, but behaviour in a stall was better than a in a Hellcat: stalls were gentle, with little wing drop and easy recovery and prononuced buffet announcing stall onset.
Corkey then went on to fly some mock combats in a P-47B against an early production Hellcat:
" The Thunderbolt's higher top speed and climbing ability was quite apparent as altitude increased. Because of this obvious asset, I decided that I would as a grumman production test pilot - a former Navy pilot- to meet me at 25,000 feet the next day to try a few combat manouvers. We squared off by closing at more than 600mph airspeed and then began to tangle. The Hellcat pilot tried to turn and evade me, but I was able to roar right past him, pull up in a wingover and get right on his tail. I had an edge because I had talked to ken Jernstadt- a double ace AVG pilot in China. The seemed too easy- almost as if he had his wheels down. After several more it was obvious that my P-47s 300 hp advantage, which gave me faster acceleration, was a benefit in high-altitude fighting capability. It seemed as though the only way a Thunderbolt pilot could be shot down was if its pilot was asleep in its comfortable cockpit "
His assesment seems to have been fairly dubious at first and then growing in confidence as the advantages of roll, speed and acceleration became clear to him.