If you're talking about the Hellcat, that's the F6F. It was the main Navy fighter of WWII. Both it and the F8F were powered by the P&W R-2800, but the F6F had a slightly lower-powered variant (2000 hp).
The F8F was was the Bearcat. They used the 34W version of the venerable Pratt R-2800. Everything I have gives an official power rating of 2100 hp. The last versions went to the P&W R-2800-30W which had an automatic variable supercharger and produced 2250 hp.
The Bear was a tremendous achievement. Developed as a true high-performance hot rod - the smallest, most efficient, most maneuverable airframe around the most powerful engine available - it is widely speculated that, had the war not ended when it did, the F8F would have quickly become the hands-down choice for best fighter of the war. Considering that the Bear had the same engine as the P-47, but was only saddled with half the weight, it's no wonder it porformed as it did! Those that flew them considered it to be a better plane in every way than anything else in the military inventory - even the P-51 Mustang. Only the F4-U Corsair outlived the Bear in U.S. naval service, serving with Marines at the controls well into the Korean War.
At little quick internet checking verified your speculation about rate of climb. Several sources indicated that the Bearcat held the the time-to-10,000 climb record for the better part of three decades.
I've seen the F8F flying with the Confederate Air Force. It's a strange beast - all stubby and hump-backed. Stranger still is the geared prop system it uses. Compared to almost every other radial-engined aircraft of the ear, the prop is just barely turning as it is idling on the tarmac. And the prop is freakin' huge! A big four-bladed affair that looks far too big in comparison to the rest of the plane. If memory serves, the only single engine aircraft with bigger props in military service at the time were the Corsair and the Thunderbolt.
Some later bombers had far bigger props, but they were being spun with the mega-monster Pratt R4360. It was an enormous affair with four banks of cylinders that grunted out 3000 hp and a mind-bending 7,500 lb-ft torque (YIKES!!). Grumman actually considered this behemoth when in the brainstorming stages. They were looking for the most powerful engine available at the time and this was it. Unfortunately, the engine assembly complete with superchargers and oil weighed in at a whopping two tons. This, and the power handling problems associated with that much torque, would have resulted in a plane with a dry weight in excess of the big P-47's max combat weight! That, and the horrendous complexity of the R4360 would have doomed the fighter. Can't remember the exact figures, but each hour of flight time was accompanied by several pre- and post-flight hours of gound crew time. Not what you want in an interceptor-style quick response fighter. Needless to say, the idea was dropped rather quickly.
Brad