According to Eric Brown, they'd fight to a draw if they ever DID fight.
The Hellcat was a bit slower, but not much. One of the funny things Corky Meyer said in some of his writings is that Grumman had the opportunity to fly the Corsair and vice versa. The Navy sent each plane to the competitor for evaluation. Corky said they used the same engine and prop, and SHOULD have been close to one another in speed.
In his evaluations, the Hellcat and Corsair were almost exactly the same when flown side-by-side. One or the other would slowly pull away when flying at the same engine settings, and it wasn't always the same plane. Interestingly, he stated that the airspeed indicator on the Corsiar always read faster than the airspeed indicator on the Hellcat, even when flying side by side at the same speed.
He also said the Corsair was slightly faster in the Main stage since the Corsair used ram air and the Hellcat didn't on purpose. Without ram, there was little chance of carburetor icing and no Hellcats were lost to carb ice around the carrier. The Corsair can't say the same.
The Corsair rolled quicker than the Hellcat but the Hellcat would easily out-turn the Corsair. The Hellcat had the most wing area of any major fighter of WWII, so that isn't surprising.
There have been a lot of nice things written about both fighters, but the Hellcat DID shoot down more Japanese planes than any other Allied fighter. This from a plane that only hit the fleet and first saw action in 1 September 1943. The Corsair was actually introduced earlier than the Hellcat, but failed its US carrier qualification tests. They only started flying them on carriers out of embarassment after the British deployed Corsairs successfully on British carriiers.
The Navy preferred the Hellcat for Pacific fighting from carriers as evidenced by their actual deployment choices. After WWII, when the Corsair and P-51 were chosen for continued duty in Korea, it was more of a case of what was available, in what shape, and with what spares in the supply chain than for any other reason.
The P-51 and F4U had the most spares in the supply pipeline. They were very good performers, no doubt, but things other than fighter performance were the deciding factors. For fighters, they were using jets. The pistons were bomb trucks and the Corsair was a good one, a bit better at hauling bombs and thus ground attack than the F6F. It got even better at ground attack when they went fron six 50-cal to four 20 mm cannons.
Heck, we were still shooting WWII munitions in Viet Nam, but we were almost out of service-level aircraft spares for the pistons when they were phased out. All I can say is that if the Skyraider had been deployed in WWII, the war could have ended sooner. That is a fact anyone would see if they had been in Viet Nam and had seen Skyraiders attack anything. It was the only plane I ever saw that could orbit friendlies in trouble for 2+ hours and either drop something or shoot something at the enemy on each and every pass.