My thought on this was not covers that we think are 'better' than the originals or became bigger hits but, rather, new approaches to the songs, in tempo, instrumentation, or attitude, that substantially reconceptualized the tunes to such an extent that the new versions pretty much became the definitive treatments. All Along the Watchtower is probably the best example. I think Bette Midler's slowed-down Do You Wanna Dance is another. Judy Collins's Both Sides Now would not qualify. Nor would James Taylor's You've Got a Friend. CSNY's Woodstock would. So too would, I think, Janis's To Love Somebody and, maybe, Bobby McGee.
Bruce