I guess this was a gripe of many with magazine reviews bitd.
I think the truth of the matter with your own C.A.T.S is none will ride similarly due to the way choices made in the build specs, for example the fork options and frame sizes will leave massive differences in how they ride, even the most subtle of changes like seatpost height and stem length would make each bike feel like a totally different bike. Comparing rigid to suspension will also contribute too.
For me, the only true way (as you say) is to have all three in the same frame size/age, with near as dam it a similar spec, or at least a similar performance of spec, so each fork having the same travel, the same stem length and height etc, gear train/component choices I think can be overlooked to a degree as this can be judged on there own merits and flaws without compromising the overview of the frame build and characteristics.
By the time these frames became available, geometry had largely settled down, each builder had there own thoughts on how to best use different brands of tubing in different parts of the bike, to give the best results for weight/strength and ride feel.
all three frame builders specifically mixed Columbus and Reynolds on these models, it would be real nice to finally have a relatively unbiased opinion of each build, and not necessarily to confirm or deny which one is better, but how they do differ.