I must ALWAYS start with my disclaimer: I am not an expert. Moreover, I am poor, and therefore do not have many high-end steels.
Oddly, I can polish AUS6 to a 'grippier' edge that AUS8 or ATS34/ATS55. Same tools: Arkansas Fine, Steel then Strop (red buffing compound). For the ATS34/ATS55, I prefer using the steel as the last step, as the stropping seems to dull and polish, rather than align and polish. The tooth, or microserration, does 'break' on stiffer, more brittle steels, but seems accentuated on some of the 'softer' stuff.
(How do you like the technical jargon to this point!)
I guess it always depends on the task, and also on how the edge is originally worked on the stone. A push sharpen produces great tooth, a slice gives a better edge to polish, a counterclockwise circular patern gives a bit of both (plus a nice-looking patina when done correctly). Then, blade shape comes into play: a Wharncliffe takes the best push sharpen edge while a skinner takes a fantastic slice sharpen edge.
The bottom line, in my humble, possibly naive opinion, is that steel matters to a degree. AUS6 vs AUS8 or ATS34 vs ATS55 vary slightly, one to the other. Now, 'surgical steel' vs the powdered metal stuff, that's a different story. But, as the majority of modern knife users don't rely on their blades for survival, rather for office work and quotidian tasks, the differences in sharpening technique can far outweigh the differences in steel composition. There are high-performance steels for specialised fields that are necessary, but for the average Joe, like me, a mid-range steel and a good technique should do the trick.
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Humbly,
RLR