In most instances of a musician re-recording another artist's song, the best you can hope to say about the new rendition is that, well, at least it's different. The notion that another artist can come along and genuinely improve on the original is rarely vindicated, especially when the original song isn't total garbage. There's also an incredibly varied opinion among music fans as to what constitutes a song being "better," since music is perhaps the most subjective form of entertainment. So don't expect to see a song on this list unless it's unequivocally considered a superior version. (Sorry to fans of Johnny Cash's "Hurt" and Muse's "Feeling Good," they're amazing but not necessarily better.)
But much like Adam Sandler is destined to release a watchable movie now and again, and Chris Pratt is bound to eventually do something to knock himself down to the second most charming person on the planet, it's not impossible for a reworking to come along that completely blows the first iteration out of the water.
These artists have the consensus where it pertains to their surpassing the song's creators, earning a Gold Medal in the (unfortunately non-existant) Music Cover Olympics.