There's a fundamental difference between these approaches which is not highlighted enough in discussions about weight loss. There is a physiological factor: weight loss is attributable to calories in vs calories out (despite those figures being difficult to obtain). Then there's the psychological factor: some diets are easier to stick to than others, and some will naturally cause you to eat fewer calories than others.

Using reported calorie information is a physiological method, and appeals to those who prefer quantifying and tracking their everyday life. Carbohydrate reduction is (in this sense) a psychological method, and appeals to those who struggle with cravings and a lack of structure.