No, no, no, don't drag me into this...
Haha joking... I think I mentioned it above, but I've done a lot of axle testing you like had Davin where I changed back-to-back and noted how the kart felt.
I did a day of rain testing once where I went through all the axles Merlin had until we zero'd in one the that made the kart work best in the rain.
The only reliable testing experience I can offer is what I personally have done. My drivers go the same speed no matter what axle is in the kart... I would say that I often notice a much larger difference in the kart when going to softer axles than when going to harder axles. I think there is a difference in the material make-up but I tend to agree with Nik when he says axles aren't "hard" or "soft", they're "springy" and "less springy".
Merlin used to have a yellow axle (hard) and a white axle (also hard) which were supposedly the same "stiffness" but the rebound in the white axle was less. I can tell you with 99% confidence that those two axles WERE different in some way. I could never make the kart stable with the yellow axle, it always hopped with it in. The white axle was much more stable so that's the one I chose every time when going stiffer on the axle.
My powers of deduction would tell me that that is probably how all axles are. There aren't stiffer or softer axles, just changes in the rates that they spring back.
I've also seen how tire wear can change dramatically with different axle compounds. One session the kart will be shredding the outside rear, and the next the graining cleans up with an axle change. So I think there is SOMETHING happening, it isn't all an elaborate marketing scheme.
Regarding @NikG's comment on cutting the axle or short axles... The short N is our standard baseline axle now in the tent. This could all be placebo, but we largely believe that the short axle helps the rear dig better in the corner. If this is actually true, my guess is that it has something to do with the relationship between the end of the axle and where the force is being applied inside the hub. The shorter axle will place more force in a different part of the hub than a longer axle will at the same track width. Something to the effect of, "getting the same result of narrowing the rear track without actually narrowing it" I guess. Whether or not this is making a difference, I'm not sure, but at this point all our N axles have been cut anyway so it's not like we can do much about it short of ordering all new axles.
For the record, I've changed axle twice this season in my kart, and one of those was to a Q for the rain. So 95% of the time I'm on the N axle. My overall feel about axles is that there are so many variables you're affecting by changing it and there's too many unknowns, that it's easier to change a bunch of other proven adjustments around the axle instead. I'd rather stick to things I can easily quantify. Also, changing axles is hard work and I'm lazy.