Rage

Ooh! Tough question! I'm hyper critical of covers in general. To me if you're going to to a cover, I want to see something different to the original. And then, it needs to be good.

I love The Herd doing I was only 19 - https://www.youtube.com/watch?v=ns82tHhJOr0 
I don't think I prefer it to Redgum's version, but it speaks to a new generation about stuff that should never fall out of our consciousness. So I really appreciate it for that alone.

The Wiggles doing Elephant is awesome! - https://www.youtube.com/watch?v=a13WnqsRc5g 
People obviously dismiss them as a gimmick or kids entertainment, but that was so well done. I actually prefer their version to Tame Impala.

But then here comes Tame Impala doing A Girl Like You - and it's next-level stuff! https://www.youtube.com/watch?v=Wt5DwYAu1ao
Definitely better than the original, even if it is a similar interpretation of Edwyn Collins.

Aurora doing Teardrop is definately up there - https://www.youtube.com/watch?v=GPTY6l_PX5k
I don't know her from anything else, which I really should fix as her voice is mesmorising.

It turns out that Sarah Blasko's Flame Trees wasn't actually Like a version: https://www.youtube.com/watch?v=cArtp8NSp0g 
Which is a shame! It's a wonderful cover and would be a contender for better than the original. She has a few Like a Version covers, though! Her rendition of Goodbye Yellow Brick Road is wonderful: https://www.youtube.com/watch?v=6wR0OgzYreU 
So is her Life On Mars - https://www.youtube.com/watch?v=tnZtVY6Lu5U 
Maybe she just does songs of my generation, which is why I love them all.

If I'm allowed to cheat, the best cover of all time goes to John Farnham with Help - https://www.youtube.com/watch?v=dv54giOSRKs 
That's probably the best cover of any song ever made. I literally grew up on the Beatles, and John totally made the definitive version of this song.