it is interesting to ponder why Germany, England and United States chose different solutions to similar problems. i suspect each country looked at what they could produce rather than look at the best solution. They all had the same problem, how to absorb increasing more power with the limits of the existing frame. The best way is to just design with a larger diameter prop in the first place. Planes like the spitfire, Bf 109, Fw 190, were limited in how large a prop diameter one could use. So limited by prop diameter, one needs more activity factor, essentially an increase in the percentage of blade area to swept area. As noted above, Germans did this by increasing blade chord, while British used more blades. The difference is i suspect is in how the variable pitch propeller mechanisms were designed. Bigger blades absorbing more power needs a more robust, heavier mechanism. More blades means more, mechanisms, maybe with little increase in weight per unit, but still the whole unit weighs more. Hard to tell if one way was better than the other.
These concerns affect climb performance more than top speed per se, which is why the use of paddle blades improved the climb performance of the P-47. Others have pointed out that altitude performance also affects the choice in number of blades, which is perhaps why the turbocharged P-47 always had four blades, while the supercharged F4U-1s got by with three bladed props.
Short answer to a complicated question.
