How to best lose weight? Low fat, low carb/hi protein, or low calories? This debate has been ongoing for at least 40 years, maybe longer, but I was too young to care back then. Now I do, and professionally, have been battered about by the various studies showing one or the other as best.
The real issue, I believe, is how to alter the caloric balance between intake and output such that physiological mechanisms either remain in place or are enhanced to maintain proper metabolism. By the latter, I mean a metabolism that is appropriate for weight control, i.e. retains muscle mass, burns calories at an expected rate/unit body weight. We know that losing weight means losing muscle means lowering basal metabolic rate (BMR) such that any additional calories are more readily stored as fat. In order to keep metabolism high enough to resist this storage, we need to include exercise, preferably resistance training, 
to our weight management efforts. If we only diet, we lose too much muscle. If we eat hi protein/low carb diets, and eat fewer calories than we need, we not only lose weight faster but we retain more muscle mass. Sounds good…but does it last? That’s the issue here.
Losing weight now is the american dream but keeping it off for the better part of one’s life is the medical and health care dream. Low fat diets are easier to engage in but not as beneficial in the short term. Low carb diets are good in the short term but this study shows they just don’t persist: http://www.healthcanal.com/life-style-and-fitness/6353.html. as this blurb from the journal itself shows, the numbers are not profound enough to satisfy the average weight-loser’s goals, but they may indeed satisfy their doctors’ goals.
Results of a randomized, controlled trial found greater weight loss at six months with a low-carbohydrate diet than with a calorie restricted, low-fat diet in 132 patients with a mean weight of 288 lbs and a high risk of diabetes. However, after 12 months, there were no significant differences in weight loss. Findings at three years were similar, but the pattern of weight change from 12 to 36 months differed. While the low-carbohydrate group lost more weight at 12 months, they regained more weight during the next 24 months. In contrast, the low-fat group maintained their weight loss. The difference in weight regain may reflect initial weight loss, as greater weight loss from baseline to 12 months was associated with greater weight gain.
Bottom line: eat fewer calories, of any sort, and be consistent through life. Oh yes, be sure to exercise too.