It's technically not an Elvis cover, his version is the best known but not this first one (I think Roy Hamilton recorded it first, but I'm not sure). I guess the Beatles probably based their version on Elvis's recording though.
Of these two versions, I definately prefer Elvis's. He had the capability to make songs 100% his own, and his version is unmistakingly an Elvis Presley song. The Beatles version doesn't sound like a Beatles song, it just sounds like a capable band working it's way through a rock 'n' roll standard.
Plus, purely as a vocalist, I prefer Elvis over any of the Beatles.