Actually neither Elvis Presley nor Jerry Lee Lewis were the first to record Jingle Bell Rock. In 1957 Bobby Helms first recorded the song while Joe Beal and Jim Boothe wrote it. Helms version is the most commonly recognized version of the song, which is in the style Rockabilly, which is a combination of Rock and Country. This version sounds much more country that subsequent versions.
Some other artists that have also recorded the song include: Amy Grant, Hall & Oates, Wayne Newton, Billy Idol, Cubby Checker with Bobby Rydell, Hilary Duff, and George Strait, among even others.
http://www.songfacts.com/detail.php?id=2421