I just came across this scenario this week. Sitting in a restaurant, I heard "Heatwave" - the version by Linda Ronstadt. Incredible as it seems, that's the version I first heard and liked, and considered it definitive, even after finally hearing the big hit Martha & The Vandellas version.
But in this case, my view changed. After thirty years or so of hearing the Martha & The Vandellas version exclusively over and over again on oldies radio, I can now honestly say that the Linda Ronstadt recording now sounded odd, out of place, and certainly no longer definitive. It was still an OK record, but clearly just a "cover" in my mind. That's how it must have sounded to the vast majority back in the '70s when Linda covered the song.
So I guess for many of us it probably goes on a song-by-song, case-by-case basis. As for "Emorio", gee, it's one song where I never really cared for ANY version. The new one is just as good or bad as the old '70s version.
Harry