I've read different things about the Atkins. Basically the Atkins diet recommends cutting out all the carbs you eat, which puts you into a state of ketosis. When you are in ketosis, your body burns "ketones" for energy instead of glucose (which it gets from carbs). If you don't eat carbs, you get no Glucose, so instead your body takes the fat that is stored and turns it into "ketones" which are used for energy. The atkins people think this is healthier than just ingesting the minimum amount of carbs needed to stay out of ketosis (but not more than that). In the Governator's book, he recommends staying just out of ketosis, and testing for it to determine whether or not to cut back or eat more carbs, or stay the same. AFAIK, this is the recommended method for most bodybuilders, and I don't see why it wouldn't work for everyone else.
Where Atkins people go wrong is protein and fat still have calories, and excess calories get converted to fat and stored. So even if you are on the "atkins diet", if you are eating 3000 calories of fat and protein instead of 2000 calories of carbs and 1000 calories of fat and protein, unless you are 250 lbs of solid muscle already, you aren't going to lose any weight.
Best way to lose fat is diet and exercise... best way to keep it off is to put on some muscle. I don't care how much I weigh, I care what my fat percentage is.