The fat man will burn more calories because he carries more weight, that is true. However, depending on their indiviual heart rates while running, one may born more calories from fat than the other who may burn mostly carbs. The higher your heart rate, the more overall calories burned, but more are from carbs.
Example: Fat man runs a mile in 8 minutes and burns 200 calories, but his heart rate is 80% of MHR, meaning he burns roughly 80% carbs, therefore burns 40 fat calories.
Thin man runs a mile in 8 minutes and burns only 150 calories but his heart rate is only 50% of MHR, meaning he burns roughly 50% of calories from fat, therefore burns 75 fat calories. It is pretty unlikely someone could run at only 50% of their MHR though, unless they were in incredible shape.
Fat man burns more total calories, but thin man burns more fat calories because his heart rate is lower. To lose weight you need to burn more calories overall, so fat man comes out the winner!