I once saw Bob Dylan cover the Jimi Hendrix cover of his "All Along the Watchtower" (he didn't play the guitar part himself).
Here's one where the original artist did another version of a song that was superior to the first. Ednaswap originally recorded the song "Torn" on their debut album. They did a radically different version later on the album Wacko Magneto. Later that year a version was released by some Australian singer.
This is the second Ednaswap version:
Here is the original Ednaswap version:
Just to get picky, while members of Ednaswap wrote the song, they didn't release a version until after Danish singer Lis Sørensen had, so, like David Bowie's "China Girl", they technically covered their own song:
Their version was shortly before Norwegian Trine Rein did it:
All four of these recording predate the Natalie Imbruglia cover. Chronologically the versions go Lis Sørensen, Ednaswap, Trine Rein, Ednaswap, Natalie Imbruglia.
Of the five versions I think the two Ednaswaps are the best, but the other three were the hits. That must have been frustrating for the songwriters, although I'm sure they were consoled by the royalty checks.