In my opinion, Atkins has some very good ideas, but takes these ideas further than they need to go.
1) Studies have shown repeatedly that the best diet to lose weight is a high fiber diet. Basically fiber fills you up, and since you cannot digest it, it just passes right through you. In fact, fiber carries with it things you normally would have digested. Thus the more fiber you eat the less food you digest, and the less you weigh. Atkins net carbs encourages high fiber foods. Thus Atkins encourages people to do what has been proven to lose weight.
2) Studies show that people eating lots of quickly digested sugar will crave more food at the next meal. For example person (A) eats a bowl of frosted flakes for breakfast, person (B) skips breakfast, and person (C) eats a low carb breakfast. Who eats the most for lunch? Most people assume the answer is (B). If you think that, you are incorrect. Person (A) eats the most for lunch and person (B) and (C) eat the same sized lunch. Why? The high level of quickly digested sugar makes person (A) much more hungry thoughout the day. Atkins avoids that problem. However in my opinion there are other (possibly better) ways of avoiding a diet high in easilly digestable carbohydrates. There is nothing wrong with the slow to digest carbohydrates - this is where I disagree with Atkins.
3) Studies show that Atkins diet does drop weight initially faster than most other diets (I haven't seen it directly compared to a high fiber diet in the same study). However after 6 months people on the Atkins diet generally start gaining weight, when people on the other diets are still steadilly losing slowly. After about 1 year Atkins is no longer the best diet. Why? Probably since people cannot keep it up, Atkins is just too strict. And it is strict in areas where there is no proof that those restrictions help.
A diet which is low in easilly digested carbohydrates and high in fiber will work very well at losing weight. Atkins does this. However Atkins just goes too far in my opinion. There is no reason have the induction phase if your goal is long term weight loss (it is fine for a short term loss - but then you have to really be conserned about heart health if you abuse it), and there is no reason to avoid the slowly digested carbohydrates.