Consider this:
A popular belief is that 1 lb. of fat contains about 3500 calories. [1] By that measure, and assuming you regularly eat at maintenance calorie level each week, eating 3500 calories below what will result in about a 1 lb. reduction in body weight that week. (which realistically turns out to be mostly fat, but can also include small amounts of lean muscle, too).
Whether you create that deficit from removing sugar, fat, carbs, or protien doesn't matter.
But that's solely for weight loss. When you simultaneously want to increase lean muscle, exercise and protein become more important. Also consider medical conditions that require adhering to certain diet regimen.
So I'm not saying that, globally, what you eat doesn't matter, only that weight loss primarily comes down to maintaining a caloric deficit. To supplement, of all the diet programs out there ... Atkins, South Beach, and even intermittent fasting ... the one thing they all have in common is that they promote a caloric deficit, somehow. And they have to, other wise they wouldn't work!
[1] Some argue the 3500 calories = 1 lb. of fat is bs. All I can say is that I've based my caloric deficit on it and it seems to hold true. I dropped my weekly caloric budget by 7k calories, and have been losing about 2 lbs. a week.