as a luthier for more than 36 years, IMO, EVERY aspect of an instrument has an effect on its tone. IME, SS frets are a little brighter than NS ones, and take more time to mill/level/recrown and polish, but once you do, their only benefit (to me) is that they last longer. personally, i don't care for the brighter tone that they create (since i'm 'old school' and set in my ways), but if you had a duller sounding bass, it might actually help it.
IMO, fret size also has an large effect on tone as it is mostly due to the amount of having more metal mass in the neck.
i refretted a '63 P bass for one of my clients years ago, that had just been refretted by a well known luthier (who shall remain nameless). the client was a pro player and original owner of the bass. he was very accustomed to his bass' tone. the previous refret had replaced the original small frets with meduim jumbo sized ones and its owner said that his bass lost alot of its 'woody' tone, and now sounded brittle and clacky. i let him play my original '62 100% stock p bass and he said that it was alot closer to how his used to sound. being the the fret sizing was the only difference, i told him that i'd remove the new refretted frets and install original sized ones. two days later when he picked it up and played it, he smiled and couldn't thank me enough. he said that it sounded exactly how he remembered it, only now, it played alot better. not being that i owned his bass for all those years, i too, could immediately tell that it lost all of its previous clackiness, and sounded much closer to my original '62 p.