You are right in that caloric expenditure is going to affect the CI-CO balance, and at a deficit your expenditure will decline due to both a decrease in basal metabolism as well as decrease in spontaneous activity.. but at the end of the day a calorie deficit is by definition the only way to lose weight.

Choice of macronutrient composition directly (and indirectly through hormones) affects satiety, and many find it easier to eat less calories by restricting carbs, but for weightloss at the end of the day a calorie is still a calorie.