I'm sorry, but this is terrible. Listen to Leonard Cohen's original, there's just no comparison. Aimee Mann has turned it into some kind of light and breezy pop ditty, whereas Cohen's version is dark and powerful, in keeping with the lyrics.
I don't agree. While the original can never be matched, Mann has a striking voice with a sense of gravity. This sounds not like a breezy pop ditty at all. It's a decent cover, in my humble opinion.