One thing (among at least a few things) I've not liked about these pull-throughs is, the striations or grind marks left by them are running parallel to the cutting edge, due to the way the edge is drawn lengthwise between the opposing grinding (or shearing) inserts. I tend to believe this leaves the finished edge weaker, as the parallel grind troughs left behind leave the edge more likely to fold over and/or break off, as would a burr. Think of the corrugations in heavy cardboard, as a comparison. It's much easier to fold heavy cardboard parallel to the corrugations than it is to fold it across them. Pull-through sharpeners are known for leaving very weak edges that need a LOT of frequent resharpening, much more often than would be necessary if sharpened on a stone. This is likely why a knife sharpened on a pull-through won't have as long a blade life, as it might otherwise have if sharpened on a stone.
By contrast, sharpening on a stone (or most powered devices, like wheel/belt grinders) usually aligns the grind marks perpendicular or at a diagonal to the cutting edge. That will leave the edge much stronger, and it also leaves much more 'tooth' in the edge, making aggressive cutting much more efficient.
Depending on the type of inserts in the pull-throughs (if they have scissor-like crisp edges in contact with the blade edge), they can sometimes pinch the thin cutting edge as the blade is drawn through. That pinching effect can literally rip or tear the steel at the cutting edge, which also leaves it very much weakened. Pull-throughs with round grinding rods or flat abrasive faces won't tend to pinch the edge in that manner; so, at least they can't do that type of damage.