Comparing John Cale's "Hallelujah" with others' would be a bit unfair. Cale has the huge advantage of his natural voice, Patti Smith once described his voice as "poems coming from his lips", so it's easy to see why no other singer could come close to his masterpiece, no matter how hard they try.
The song is about love which has soured and gone stale. Cohen used a lot of religious imagery, including references to some of the more notorious women in the bible. Here's some lyrical analysis:
"You saw her bathing on the roof, her beauty and the moonlight overthrew you" - Bathsheba, who tempted the king to kill her husband so he could have her.
"She tied you to her kitchen chair, she broke your throne and she cut your hair" - Delilah, who cut off Sampson's locks that held his superhuman strength.
"But remember when I moved in you and the holy dove was moving too" - This could be a reference to the divine conception and Mary.
The lines referring to the immaculate conception can also be interpreted as having a sexual connotation: "And every breath we drew was hallelujah." http://www.songfacts.com/detail.php?id=2504