Obviously music is a matter of taste and it is going to be common for someone to hear a cover by a band or artist and like the cover better than the original but other than that there isn't much to support the cover being better than the original. My example of Jerry Lee Lewis doing "Over the Rainbow". That pretty much just comes down to me since not many people have ever heard Lewis's cover of that song including Wikipedia.
So maybe we should narrow the field and rather than saying covers that are better than the original or that eclipsed the original, maybe we should say covers that are better than AND have eclipsed the original in terms of critical reception, sales, popularity etc.
I think the "AND" is important because there are notable covers that eclipsed the original but are still pretty awful..."The Night They Drove Old Dixie Down" by Joan Baez being a prime example. She made it a hit song but she also made it an awful song.