First of all, talking about burning solely fat during exercise isn't quite right. Perhaps more correctly, we need to just talk about calories as a whole. Both forms of exercise burn calories and, if in a caloric deficit, some of those calories must come from fat stores. If we're talking about calorie use, it really depends on the intensity and repetitions of sprints. Obviously, due to the high intensity of sprints and HIIT, the duration must be much lower than that of steady state cardio. However, because anaerobic energy systems (phosphagens and anaerobic glycolysis) are dependent on oxidative processes to be restored, there is an increased demand for both oxygen and energy utilization post-workout. This excess oxygen consumption and energy creation is utilized to restore/reform ATP, creatine phosphate, and glucose. This is called the excess post-exercise oxygen consumption (EPOC). The EPOC is well studied. It is increased as the intensity and repetitions of sprints increases. However, sprinting rarely burns as many true calories as steady state cardio. It does increase AMPK levels (a marker for oxidative stress and accommodation) higher than steady state cardio, which may help explain why HIIT significantly improves one's endurance even though it seems like an unrelated feat.
Also, to address your question about raised metabolism and muscle: carbohydrates and fat are very easily available as energy stores. Carbohydrates are dominantly used at higher intensities while carbs and fats together are used at lower intensities. Unless your body's glycogen stores are depleted, the amino acids in muscle mass tend to be untouched. If you're working out for periods greater than one hour, you should eat/drink some simple carbs to prevent muscle breakdown (since it gives the body an easier alternative to protein breakdown). No matter if you're doing sprints or steady state cardio, eating a meal high in carbs and protein is essential afterward to prevent post-exercise protein degradation.