In principal you are right Gscholz. The primary benefit of water cooling over air cooling is the minimization of hot spots in the cylinder.
But everthing I've read says that a piston engine run at anything near rated power must be run in a rich fuel mixture, water or air cooled. That doubles the amount of fuel used per pound of air introduced into the cylinder.
It could be the case that fuel consumption at max horsepower (without wep) with a water cooled engine will be less than an air cooled one, but I've not seen any data on US engines to confirm the difference is dramatic.
As I said, the Allison liquid cooled v12 experiences a significant increase in fuel consumption at higher output settings precisely because the fuel mixture goes to auto rich. You also see this with specific engine charts for the P51 using the Merlin.
Here is an example of curves from US specific engine charts:

In this chart (before the carburetor change) the R2800 is a hog at high outputs. The increase for the Allison is about 50% and for the cyclone about 80%. These are rough numbers as the cyclone data is from the Curtiss Wright manual and does not incorporate the installation. The Allison is for the P-38. At peak outputs, the advantage in specific fuel consumption for the Allison over the Twin Wasp is only about 13% and for the Cyclone it is only about 8%. Even for the R2800, the disadvantage is only about 18%.
On the other side of the ocean, if you look at engine charts, such as the ones posted in this thread, you see fuel consumption curves that are much flatter than for US charts. It's true for air cooled engines too. I've seen charts on the BMW 801 and the ASH82 FNV that exhibit the same characteristics.
Fact is that no one during the war ever said that the Germans or Russians had engines that were twice as fuel efficient at rated power as the American engines (let alone Bristol or RR). So I have to wonder if the method of calculation is different than for the US charts.
-blogs
Originally posted by GScholz
Pyro on the F4U4:
The air-cooled radials were designed to operate at cruise or normal power, just like any other engine. However they were less suited for emergency power because they easily overheated. A liquid-cooled engine has a rather large engine block made of metal that the cylinders are bored into. Metal is very effective in transferring heat away from the cylinders and transferring it to the coolant through the coolant-loop.
An air-cooled radial only has a thin skin of metal with cooling fins surrounding the cylinders, which is easily overheated compared to the massive engine block of an inline engine. That's why I believe they had to use very rich mixtures at high power settings to help cool the cylinders, piston heads, valves etc.
The Radials were somewhat fuel efficient on low power settings, but still I have not seen any data on a radial that matches the efficiency of the DB and Merlin or indeed any other inline. The radials were favoured for their reliability, toughness and low weight.