Prolonged fasting (not eating for 3+ days) speeds up the metabolism and more energy is spent during activity. Calorie restriction (eating less than the body requires) slows down the metabolism, so less energy is spent during activities.

The first screenshot shows the data of my 1 hour weight lifting in the gym from yesterday (17 days without food, 80 kg). The second screen is a 1 hour workout from 43 days ago (eating usually, 90 kg).

Even though my weight was 10 kg more, which should have increased my energy expenditure, the workout in the fasted state has spended more. It even shows in the average BPM. And the intensity of the fasted workout was also lower.

Putting aside countless health and other benefits, fasting is the best method of weight loss.