For an amino acid from an "average" protein, ATP is produced at 33% efficiency. If the amino acid is incorporated into a protein and must be later hydrolyzed, ATP production is reduced to 27% efficiency.
Comparitively, glucose, directly oxidized, produces ATP at 38.5% efficiency. If glucose is incorporated into glycogen and later broken down to produce ATP, the efficiency drops to 35%.
(Thermodynamics of weight loss diets; Eugene J Fine, and Richard D Fienman)
(Nutrition & Metabolism)

This explains why fat is the preferred fuel (very efficient) for day to day activites and low intensity exercise. It also helps to explain the "metabolic effect" of low carbohydrate diets as compared to iso-caloric higher carbohydrate diets. Protein is a very thermogenic (produces extra heat during digestion/utilization) nutrient as compared to carbohydrate. The processes of digesting and converting protein to ATP are energy costly, this makes your diet "inefficient" and helpful for fat loss.