I like Cohen's. It's different from all the Wainwright-style covers, and I once heard he'd written over a hundred verses for it that he alternates on concerts. I wish they were available somewhere, but I suspect I would have had to have been there.
I'm not enough of a fan to know how many of those verses he did sing in concert, but I do know that I have two recordings of him singing the song and they only have one verse in common. Weirdly, this verse ISN'T in the Jeff Buckley version. And it's easily my favorite:
And even though
It all went wrong
I'll stand before the Lord of Song
With nothing on my tongue but Hallelujah
The reason I like Cohen's the best is because of the backing singers. I think this song works best when there's the graceful and harmonious support of the backup singers... it adds to and "load balances" the hugely majestic tones of this song! I think when KD Lang or anyone does it solo, they're taking on too much, and while they might do a fine job, it's a lot for one person to sing. Just my thoughts!