My thinking about covers is it can't be better than the original unless it's different. Doing a tribute to the original is all good, but it's a forgery of sorts. If a band makes the cover their song, yeah, it can definitely be better.
Thinking along those lines, the original of this song, by Jonathan Richman (a favorite of mine) is hardly listenable. This cover is really cool, if you are into that type of neo-psychedelia.
Room full of Mirrors :The Pretenders (Jimi Hendrix)
I like both, but it`s easier to have a crush on Chrissy, and the band really does the song justice IMHO.