I thought I'd start this thread with the theme of finding covers of songs that reinterpret/reveal the original song in a new light (or just is better than the original).
Edit: I've cleaned up this first post as it wasn't being formatted correctly - I posted each entry individually below instead (& included the original version too)
And just a left field one - Don McClean doing Mountains of Mourne - a classic Irish ballad normally just rattled through, but McClean exposes the poignancy & sadness (all Irish ballads have that in heaps) in the song
There are lots out there - some "new" songs are a rediscovery of an old song that a lot of the listeners don't realise