Q: Does the atkins diet work for some people because protein is less fattening than carbs or because they are consuming less calories when they go on that diet?

A: The theory behind Atkins diet is that by depriving your of carbs you force it to burn fat reserves for energy. It does work to a degree, but it also has a host of negative side-effects:

• As you can guess if you've been reading my responses to other questions, a carb-deprived body will turn to burning muscle for energy in addition to burning fat for energy. The ratio of muscle-to-fat loss will again vary widely depending on genetics and exercise regimen followed.
• The diet is extremely strict, especially in its first weeks, and is very tough to stick to. If Atkins is not followed strictly, then the whole point of it is largely lost and it becomes just another calorie-deficit diet.
• Atkins diet will often leave you completely devoid of energy, again especially in its first weeks. This also makes it very difficult to follow an exercise routine while on this diet.
• By rigidly restricting carbs, Atkins followers risk depriving their bodies of vitamins and minerals that they typically get from vegetables, fruits, and grains. I feel very strongly that popping a few multi-vitamins is not the same as getting natural nutrition from food.
• Another consequence of rigid carb limitations can be digestive and bowel movement problems. Once again, a common approach is to turn to any number of drugs or supplements for that which I feel is a bad idea for your health in the long-term if it can be avoided.
• Atkins does not, as far as I know, distinguish between healthy and unhealthy fats. I very very strongly advise avoiding using oils for high-temperature cooking (frying) because oils oxidate and turn into what you've probably heard of as 'transfatty acids' which are bad news. Same goes for foods containing hydrogenated oils (basically, the same thing).
• Atkins diet naturally leads to getting most of the fat intake from animal sources. While there's nothing wrong with animal fat as such, it is mostly saturated fat, while ideally you want to be consuming mostly monounsaturated fat (olive oil) and omega-3 polyunsaturated (salmon and other fatty fish as well as flax seed).

But even forgetting about possible negative long-term health consequences of Atkins, it is still not the best choice for most people simply because it will aggressively burn muscle along with fat. If you are not grossly overweight and are looking to lose less than 50 pounds, I suggest low- to moderate-carb diets (along with exercise, of course) such as described in the nutrition article instead of Atkins.