I own 15 or so official Saturn console controllers in addition to two Authentic USB ones from before the knockoffs and crap flooded the market. A heavily worn old Saturn controller feels so different to a fresh one, and I have ones of all types in my collection. As for the Retrobit ones, I have taken to playing my Saturn exclusely with the 2.4ghz one.
Yeah, that's likely part of the problem, but I am not sure it can account for all of it, because back when I used to use those you could get in the 90s heavily, I had six myself (on top of those friends had), and swapping to a fresh one didn't feel so "off" like all of those I've tried since. I literally used one of the originals 3-6 hours
every single day for about four years straight almost exclusively with fighting games, so I'm pretty acquainted with them. More recently I would play MvC2 at a friend's house on his Dreamcast using an original Saturn controller regularly up until 2008 without any issues and even won a local tournament using one in 2012. This isn't one of those faulty memory/you're just older now and can't do it as well situations either because I generally don't have any issues acclimating to a new controller or stick as long as it's relatively accurate.
Like just recently on Wednesday night when I was playing X-Men vs Street Fighter
on the Saturn, dashing felt extremely questionable. Maybe it was not really a problem so much with the D-pad itself, but input lag that was introduced from playing via bluetooth, but I just kept finding myself not dashing at least of a third of the time. This was extremely noticeable with Chun Li, who I used to play super aggressively as well as trying to do Gambit's infinite, which is one of the really easy ones to pull off.
Truth be told, I'd rather use my
Hitbox styled TE stick now with fighting games, but I find them nearly impossible to use with the older Capcom games, or just any that don't use shortcuts, and since Windows 10 broke my ability to use it on PC anyway, I can't even use it anymore with retro shmups.