With Natalie Imbruglia's take on the Ednaswap song "Torn", I'd suggest that we are getting into the relatively small list of "covers that sound better than the original" - regardless of whether you consider the "original" to me Ednaswap or Lis Sørensen.
This song was an instant hit when it came out. Actor Imbruglia wasn't well known as a singer (to me, anyway), but she has a great voice and this is a superb pop production from one-time producer and member of The Cure, Phil Thornalley.
Although written by Ednaswap (Scott Cutler and Anne Preven) with producer Thornalley, the first released version was by Danish singer Lis Sørensen. Ednaswap recorded it themselves, though without the pop sheen of Imbruglia's version, and there were other takes before Imbruglia brought it to the masses with her perfect version.