Since getting some great advice here on BFC some months ago I think I've come to appreciate some of the complexities of stropping. Not only is softness or "give" of the leather or other strop material and any backing a factor but the nap of it is as well. Then you've got the pressure used when stropping, and how the geometry of the blade and edge are going to affect how that pressure is distributed and how the strop is going to squish/curve/give as a result. This really hit home when I became interested in Scandinavian ground blades .... with their very wide primary bevels they're very easy to strop because they're easy to control, plus the pressure is distributed across a much larger area than with other edge grinds.
Though I've never used an EdgePro I think I see how such good results are attained with the tape, which seems similar to stropping - the system gives much better control than you can get freehand, there's very little give to the tape and it has little or no nap. So basically the EdgePro lets you to follow a bevel very accurately, even a narrow one, hence sharpening and not dulling.
But I've also come to realize lately that with sufficient skill you can achieve sharpness that's as good or greater than with freehand stropping using a fine ceramic Sharpmaker or CrockSticks, the trick is to use very minimal pressure and patiently bring the edge to a high level of sharpness. After a lot of work and practice lately I can get nearly any decent blade push cutting newsprint 3" or more from point of hold just using ceramic, a couple even rivaling Ben Dale-level sharpness. And this edge is consistent along its entire length, much better than what I can do with stropping on leather. IMO this is mostly due to consistency, which is much harder to achieve stropping freehand with knives that have narrow edge bevels.
Just food for thought .... the bottom line being any number of things could be going on when stropping depending on factors mentioned, which explains why different people seem to have different success with different techniques.