| I don't know about the difference between the 2 diets, however the atkins diet works because you eat less calories on it...
they did a study (I believe it was sweden/norway), where they set up a shop, where all the foods were carefully measured, so the exact calorie content of the food was recorded. The subjects then were required to buy all their food from the shop. The subjects were divided up into various groups -
the group that ate a restricted carb diet (it was not as extreme as the atkins), actually ate fewer calories than the other groups.
one anomalie came out of the study was the group that ate nuts - despite an apparently high calorie intake they actually lost weight...
...the reason they concluded was that nuts are an unprocessed food, so that it is very hard for your body to extract all the nutrients from it - ergo you may eat a load of nuts, but you aren't getting the calories. This also means that for those promoting the health benefits of the nutrients in nuts, is not as good as it would seem on paper.  | 
