The comparative evaluation of machinery plant design and installation, which is what I think is being attempted here, is a difficult -- and perhaps essentially intractable -- one.
The literature directly comparing two or four shaft vs three shaft propulsion arrangements is rather meager -- there were relatively few three shaft arrangements completed -- and often inconclusive. A fair amount revolves around the physical placement and size of the propellers and how they interact with the hull, the surrounding water, and themselves. It appears to have been somewhat difficult to balance three-shaft arrangements with regard to hydrodynamic considerations insofar as the center shaft is typically operating behind a main skeg whereas the wing propellers are not. The propellers behave differently in that regard, insofar as the flow to the center propeller is usually somewhat disturbed by the wing propellers, which are usually somewhat farther forward, and because the center propeller is aft of a vertical skeg, which can lead to vibration problems as the blades cut across the flow lines. The net result is that the center propeller can often take quite a hydrodynamic beating in sharp high-speed turns. Because the center propeller is working in a different flow field, it is (or at least was) common to make its pitch, diameter, or rpm different from that of the wing propellers in order to maximize efficiency and reduce problems with vibrations, etc. This was true even in four shaft arrangements, where variations in pitch etc. from the inboard set of screws to the outboard set was not uncommon at all.
Bismarck appears to have been somewhat unusual insofar as -- at least to my knowledge -- all three of her propellers appear to have been essentially identical.
Overall, it appears that if the design is done properly, there is relatively little to differentiate a good three shaft from a good two or four shaft arrangement.
So far as machinery weight and horsepower issues are concerned, the main problems, as others have noted earlier, revolves around the precise definition of exactly what items -- or, if the analysis is volumetric, what spaces -- should be assigned to the group 'machinery'. Our discussions on this thread seem to have only included boiler rooms and turbine rooms, but there are quite a few spaces other than that that might be legitimately be included as 'machinery spaces' as well. This is true of many ships where often the only thing one has to go by are the labels (names) assigned to various compartments. Also, there is often a good deal of ambiguity associated with exactly how the noted horsepower was actually measured, or whether it included overload or 'hotel' factors as well. Plant output and Shaft Horsepower are not necessarily the same thing. A small adjustment to propeller geometry can have quite an effect on exactly how much horsepower can actually be delivered into the water, whilst changing the machinery weight hardly at all. A small change in water temperature, which affects condenser efficiency, can have similar effects as well.
Unfortunately, most figures quoted tend to come from secondary sources, who tend to try to compress the results of perhaps a hundred pages of measurement data into a couple of lines in a table. While they can be considered rough guidelines, it's difficult to compare them across international lines in other than a fairly general manner.