The Corsair was superior in roll, turn and landing speed - all related to 10% lower wing loading. The Mustang was superior in acceleration, climb, speed, zoom climb, dive all related to 2/3 Drag values compared to Corsair.
I suppose the definition of "close" needs some scrutiny. As to "all speed", the relative turn capability of the Mustang matched the Corsair at high altitude and the roll rates matched at high speed. The comparisons basically need to be period vs period such as F4U-4/-5 vs P-51H; F4U-1 vs P-51B/D
I'm totally clueless but I'm curious, how come the turning capability of P-51H matched F4U-5 at high altitude?, I mean wouldn't the lower wing loading of F4U-5 mean it also have more lift to spare, especially at high altitude where there is less air and wing loading is more important?.
I found some overlapped chart which seem to indicate that F4U-5 is much better than P-51H in term of speed at high altitude, but I have no idea why though? better engine?
Also, do you have any roll rate chart of F4U-5 and P-51H? I assume that they are same as previous version?. The only piece of anecdote data I can find was that they did some test between F4U-1 and FW-190? and allegedly F4U-1 roll much better than FW-190, and since FW-190 rolled better than P-51, that mean F4U all version will roll better than P-51H?.
Overall, it would seem to me that F4U-5 is superior to P-51H in almost every single aspect of a fighter:
Armor and survivability:
F4U have much better armor, it was the only WW II fighter with armor that can stop 0.50 cal bullet, and of course the radial air cooled engine survive bullet much better than the liquid cooled engine
Turn rate:
F4U-5 is a carrier born aircraft thus has much lower stall speed compared to P-51, therefore, it should turn much better than P-51.
Roll rate:
F4U rolled better than FW-190, and since FW-190 roll much better than P-51, it can be concluded that F4U-5 roll better than P-51H
Weapons:
F4U-5 is equipped with 4x20 mm cannon with better destructive power and longer range compared to the 6x 0.50 cal machine gun on P-51H
Ceiling:
F4U-5 has higher service ceiling than P-51H, probably comparable to something like Ta-152
Speed:
P-51H is faster than F4U-5 from sea level till around 13500 ft.
F4U-5 is faster than P-51H between 13600 ft to 18500 ft
P-51H is faster than F4U-5 between 18600 ft to 24500 ft
From 24500 ft and up, F4U-5 is better.
So overall, F4U-5 could cruise at higher altitude where P-51H can't compete in speed, and if P-51H loiter at lower altitude then F4U-5 pilot can just dive on them
Climb speed:
P-51H climb better than F4U-5 till 27000 ft, then after that F4U-5 climb better
Dive speed:
All version of P-51 dive better than all version of F4U, so technically this could give P-51 pilot option to run away