An effective, active CAP duty requires good guesses and estimates for enemy activity. It's literally a Combat Air Patrol.
Floating around a CV, seeing an enemy plane, and going climbing into him to catch him as he soars into the CV is largely ineffective - at least, if there is a determined CV hunter who knows how to hit the ships with great accuracy and get out alive, then that kind of CV defense will not work.
In that aspect, altitude is something that should be prepared well before any enemy approaches the CV. In that sense, climbing ability is not much of a concern for CV CAP.
Personally, for dedicated patrol duties, something with a long flight time is preferable - the F4U-1 with DTs naturally become a good choice for me.
As long as you've guessed the enemy's intentions, a F4U-1 w/DTs on a patrol duty is pretty much ideal for running down a plane, intercepting him out of the sky, and then resuming the patrol, whereas any other CV planes are usually pressed to a few such interceptions attempts, and then have to rtb because there isn't enough fuel to climb back up again and wait for more enemies.