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 Ednawap (Scott Cutler and Anne Preven) with producer Thornalley, the first released version was by Danish singer Lis Sørensen. This take was named Brændt (Danish for Burned).
Ednaswap recorded it themselves, though without the pop sheen of Imbruglia’s version, and there were other covers before Imbruglia brought it to the masses with her perfect version.
Another Ednaswap song worth checking out is The State I’m In, either the original, or Sinéad O’Connor’s cover.