I just heard the man himself sing this song - Leonard Cohen. His version these days is very close to the way Jon sings it, though he has a very different voice.

It used to be just him and a guitar but last Friday was a gorgeous version with a superb backing band.

I have no idea if there is a written quote crediting Cohen with saying that the Bon Jovi version is his favorite though. Though there should be - it's my favorite version and I first heard that song in 1991 (I think) on Cohen's album.