With the comparison above, the P-47D outclimbs and outruns the F6F-5 at all altitudes. Notice that this is a 56" boost P-47, which is far worse than a 70"boost P-47D near the end of the war. A P-47D with 70" boost, 2700rpm and improved water injection significantly outruns and outclimbs the P-47D with 56" boost, especially at lower altitudes.
From what I've gathered through official test reports and anecdotal evidence, with similar horsepower ratings and configuration (with wing pylons or without) there wasn't a whole lot of difference in speed between the two types at moderate altitudes. And you have to remember that 56" of boost is while using water injection. You must compare it to an F6F-5 that is using water injection as well or it's not a fair comparison (the added boost can have a noticeable affect on both top speed and climb rate).
One more inconsistency with your comparison is that the F6F-5 is configured with wing pylons/rocket launchers while the P-47D in question is in a "clean" condition. By the spring of 1944 it was common practice to operate the P-47D with wing pylons. This would obviously reduce the maximum speed of the aircraft in your example (I've read that the P-47D would have a loss of at least 15 mph with these rather large pylons installed). According to NAVAER documents the dual pylon and rocket launcher combo on the F6F-5 reduced attainable speeds anywhere between 11-16 mph, depending on altitude.
Here are graphs that specify the maximum speed and climb of a typical P-47D with wing pylons installed. The line to the far left in each graph is the performance of the aircraft without water injection (52" Hg). There's a definite performance drop. In fact, the F6F-5 from your example out climbs the P-47D up to 20K feet and speeds are much closer at low altitude:
http://www.wwiiaircraftperformance.org/p-47/p47d-44-1-level.jpg
http://www.wwiiaircraftperformance.org/p-47/p47d-44-1-climb.jpg
Using these same graphs compare the performance of the P-47D with 56" boost (second line from the left on the graphs) to an F6F-5 in "combat" power (water injection). Both of these airplanes utilize wing pylons, with the Hellcat having an additional six wing-mounted rocket launchers (this was a very common service configuration for the F6F-5). Once again the Hellcat out-climbs the Thunderbolt up to medium altitudes and has similar speeds up to 10,000 ft. Even with the P-47D at 64" Hg (no water injection/150 octane fuel) the Hellcat will out-climb it low down but does begin to lag in speed somewhat. To remain competitive at this point the F6F-5 would have required similar water jet modifications that were applied to the P-47D (or the higher octane fuel) in order to achieve similar boost pressures. Be aware that figures for the F6F-5 are in knots so they must be converted to mph:
http://www.wwiiaircraftperformance.org/f6f/f6f-5.pdf
One other thing to consider is that if the Hellcat were tasked to regularly operate in European skies it would have most assuredly been supplied 150 octane fuel. The resultant increase in allowable boost would have further improved speed and climb of the Hellcat below 18,000 feet (it's normal critical altitude while at war emergency MP). However in the Pacific theater 130 octane fuel was deemed sufficient for the job at hand because Japanese aircraft performance wasn't on par with their European counterparts. The use of this higher octane fuel w/water injection by the Hellcat would have allowed for a more honest comparison between the maximum attainable performance of these two airplanes.
It's difficult to directly compare the value of these two airplanes. The Hellcat was a carrier-based airplane that would have had a difficult task escorting Flying Fortresses at 25,000 ft, while the Thunderbolt could never operate effectively as a carrier fighter. Outside of roll performance the Hellcat was far more maneuverable at medium altitudes, but that all changes as the airplanes climb to higher altitude. Only then can a Thunderbolt use it's superior performance against the Hellcat and prevail in a dogfight. Two very different missions for two very different aircraft.