Renrich, let's stick to the statistics at hand as they are far more of an apples to apples comparison of the singular and limited issue of survivability between the Hellcat and Corsair under controlled circumstances. We have a huge data pool, same period, both from same carriers, both having suffered AA hits. (Prior to 1945 F4U's hardly operated from carriers so their losses are not comparable to those suffered solely in carrier operations. Also, as Joe B pointed out on another forum, there was more scope to nurse a damaged landbased plane back to base considering the greater risks of a carrier landing in a damaged plane. Further, as JoeB pointed out, the Hellcat did not fly along with the Corsair in Korea but the Skyraider did and the oil cooler vulnerability of the Corsair showed up prominently there too.
41% of carrier based F4U's
actually hit by AA fire became losses versus 26% of carrier based F6F's that were
actually hit by AA fire in 1945. (source "Naval Aviation Combat Statistics"). That's more than a 50% greater chance of becoming a loss under circumstances of actual AA fire hits. Moreover, you could argue that the Hellcat had a greater chance of getting shot to Hell to begin with because it was slower and thus an easier target.
The US Navy apparently thought it worthwhile to comment on the data and the proper conclusions to be drawn as they related to the Corsair and Hellcat with respect to survivability. From the report itself at page 58:
Thus comparisons are valid between the carrier F6F and F4U totals because they generally operated from the same ships during the same periods.
...
Certain tentative conclusions may be reached from these two tables:
(a) The F6F was slightly superior to the F4U in combat, apparently chiefly because of its greater ability to survive damage.
You will note that it was the United States Navy, as opposed to several individuals on the web regurgitating the same thing they heard someone else and each other say, that said that the Hellcat had a greater ability to survive damage. That assessment was not based on anecdotal accounts but from a huge amount of data collected according to objective criteria.
(I remember when you were more than willing to argue an unsubstantiated assertion that the USAAF had admitted that the Corsair could take more punishment than the Thunderbolt.

Surely you aren't going to now argue with the US Navy's verifiable declaration concerning the Hellcat and Corsair.)
Moreover, the Navy declared that the Hellcat was superior in combat to the Corsair in the valid apples to apples comparison (see the data limited to carrier operations in 1945). Now the Corsair could
smoke the Hellcat in just about every combat maneuver, climb, speed and roll. And yet still, the Hellcat was adjudged superior in combat. How can that be?
Apparently, chiefly because the Corsair had more than a 50% greater chance of becoming a catastrophic loss under circumstances where actual AA fire was suffered.
Again, the culprit appears to be the oil cooler. The other R-2800 powered fighters do not have these interesting tidbits inserted into the pilots manuals.
The Pilots Flight Operating Instructions for the F4U-4 (October 1944 T.O. No. AN-01-45HB1) warned that there was only enough oil for a maximum of ten seconds of inverted flight. Also, where there was damage to an oil cooler with resulting loss of oil, neither the oil pressure gauge nor the oil temperature gauge would register the change in pressure or temperature until all of the oil was out of the system. (See Manual at page 10) Pilots were warned during combat to check the oil coolers and trailing edges of the wings often for damage that could prove catastrophic.
I have checked the pilots manuals for the P-47 and Hellcat and no such caveats or warnings are present. Nor have I ever heard of any noteworthy vulnerability of the oil cooling systems for either.
As JoeB has pointed out, the oil cooler vulnerability issue is further supported by reports from those who fought in Korea. I have been reading various references to the vulnerability of the oil coolers in Corsairs elsewhere on the web (as I am sure you have) as well.