One of the things that interesting to me about them is that John Cale did a cover of the Cohen song ... and then everyone else covers Cale's version.
I think that Rufus Wainright's version is the closest to Cale's and The Rubes have a version that is more piano.
In a quick scan through iTunes, I haven't found any (yet) that use Cohen's lyrical arrangement rather than Cale's selection.
(edit) Matthew Schuler appears to be a proper Cohen cover (complete with the female backup voices on the Hallelujah choruses over organ). It has the "Lord of Song" verse, but it didn't have the "holy or the broken Hallelujah" verse.
The Canadian Tenors also have a composition that appears to draw from the Cohen rather than the Cale arrangement.
Tori Kelly's cover has all the verses that I recognize from Cohen's version.