Been listening to two versions of this song, one sung by Martha Wainwright (original) and Cheryl Cole (cover). I can see why many people would prefer Cole's version because her voice sounds more nasal, more pleasing to the ear. Wainwright's voice is a lot sharper, and reminds me of Kate Bush. Wainwright's voice is not what you'd normally hear in radio pop songs.
I much prefer Wainwright's version. The intensity of her voice is a clear contrast to Gary Lightbody's, which is also quite nasal. When I listen to them sing, I can hear the excrutiating yearning in their voices. If their voices matched, that effect would be lost because they'd sound too well-blended, which is what I hear when I listen to Cole's version. When Cole and Lightbody sing the duet, her voice almost overpowers his. When Wainwright and Lightbody sing, his voice sounds more velvety, an effect that I find very emotive for this song.