It depends on your goals and lifestyle - particularly your activity level. Atkins is no good for anyone who wants to lift weights or do any kind of "excessive" exercising (e.g., is not a couch potato). I tend to think of Atkins as a diet for someone who doesn't workout....but that's just me.
CKD is designed to allow for a few days of balls to the wall training (usually the two days following carb-up) - yet still allow a ketonic state to be reached during the week (the low-carb phase).