I think it would be prudent to do both types of exercise for fat burning. LiT will burn fat directly as there will be more oxygen going spare (ie you are not out of breath). the body HAS to have oxygen to burn fat, it cannot do it without it. When you are training at a higher intensity then the body connot use the oxygen to burn the fat as it is using it to supply the muscles. This means the body then turns to carbohydrates for its enegy. This is where a lot of the confusion comes in because people assume running is an aerobic exercise, and if done at a certain intensity level it will still require oxygen, but as the intensity level increases, and the body cannot supply sufficient oxygen, it will switch to using a higher percent of carbs and a lower percent of fat for fuel.
While doing aerobic exercises, your body uses a higher percent of fat for fuel. Approximately 60% of the total calories burned during a low to moderate aerobic exercise are from fat. but as the intensity level increases, the body switches from using fat as the primary source of fuel to using carbs. A higher intensity workout will use only approximately 35% of fat for fuel. A HiT workout the percent of fat may only be 5% of total calories burned.
But you burn more calories doing the higher intensity stuff (and in a shorter period of time), so this will put you in more of calorie deficit over a 24 hour period, which means more weight lost...
I definitely think people should do both if they can, if they have 60mins to give walking on a treadmil great do it and burn the fat directly, if you only have 20 mins to do it then do HiiT and get the same calories burnt... I think either way as long as you are doing it then you will be fine... just my 2p worth