Those people balloon back up for a couple of reasons. Most of them weren't losing 15lbs to get from 12 to 8% bf.. They were seriously obese people that used a ketogenic diet because their eating habits were bad enough to get them that big in the first place. I know this because my eating habits are what had me at 270 2 years ago. They never address the problems that got them in the position they were in. Also, remember that the Atkins diet is an SKD not a CKD. In a standard ketogenic diet, you stay in a state of ketosis for an extended period of time. Even though you do eat some carbs, there is never a time for carb up. Because of the appetite suppression from the ketones, it's easy to let your calories get really low, and thyroid function suffers. Ultimately, months later, you begin to eat carbs, and you are very insulin sensitive and your metabolism is down. You've deprived yourself of carbs for so long, it's easy to overdo when you can eat them again. If you don't follow the gradual readdition of carbs as he lays out, you run the risk of gaining back everything you lost and then some. With a CKD, though, the weekly carb up keeps your metabolism and leptin levels up. You don't stay carb deprived for more than 5 or 6 days at a time, and there is no big extended calorie deficit to worry about. In the long term, a CKD is much better from that standpoint.
That being said, both have the potential danger of helping people lose weight without addressing the dietary concerns that got them fat in the first place. For long term wellness, a balance has got to be reached where you can learn to eat a healthy diet and maintain your ideal weight. This may have rambled a little, but I hope it answered your questions.