They are both good, however, I have to go with Jerry Lee Lewis on this one - that blue-eyed soul just reaches down into your heart. He surely was and is talented. Too bad he lived such a reckless life.
I think The Killer has more hurt in his voice on this song and thus gives a more soulful performance. To be fair to the Ray Charles version, the lush orchestration and backup singers make it a bit too slick and polished sounding. In contrast, the rawness and sparseness of the JLL arrangement serves to give it an edge in that regard. All IMHO and YMMV.