It's difficult to compare two propellers since so many parameters are different. The basic aerodynamics of a propeller is not much different from the aerodynamics of a wing or rather a number of ½-wings. There are a few more components such as swirl (outwards acceleration of the air flow) but the predominant factor for aerodynamic efficiency is the aspect ratio (for a propeller = diameter² / blade area). If a propeller has all parameters equal, except the number of blades and the chord of the blades (to maintain equal blade area), the higher the number of blades - the higher the aspect ratio - the higher the efficiency.
The germans must have known about this and other considerations must have dictated their choice of less efficient propellers and my bet is the gun synchronization issue.
There are many examples of landing gear design to accomodate the longest possible leg in the wing. The shock absorbers of twenty-series Spitfires were compressed when the gear was retracted. The F8F Bearcat had "articulated" legs which were "folded" into the wings. The shape of the F4U Corsair wing was to acchieve higher ground clearence with shorter landing gear legs. This indicates that the diameter of the propeller is vital and the higher the diameter - the higher the aspect ratio at any given number of blades.
Christer
Edited:
Propeller tests to determine the effect of number of blades at two typical solidities