Walking burns fat and oxygen, as intensity increases (the exercise becomes more anaerobic), less energy is burned from fat and more energy is burned from the glucose/glycogen stores in your muscles e.g. sprinting. Running at a faster pace means you will burn more calories, yes this will come from your muscle energy stores but burning 500 calories of energy means that your body will have to replenish these stores with 500 calories worth of food, whereas walking/jogging for the same length of time may only burn off 50 calories directly from fat. Therefore I suggest HIIT training, it is thought by many as the best method of losing weight when exercising. HIIT consists of sprinting or high intensity exercise for short periods of time with a short rest in between.