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Best Way to Burn Fat on the Treadmill

Does low intensity burn more fat or the high intensity? I did a quick google search and found that both do but at different rates.

Lower heart rate workouts the energy system of the body favors fat for energy,but you don't burn a lot of calories.  As yoour heart rate rises the body moves from burning more fat to burning more carbs (sugar as you called it) until at or near your max heart rate you switch to almost pure carbs as fuel.

Here is the catch, at lower rates you burn more fat but not many calories and at the high rate you burn more carbs but not much fat but a lot of calories, so in reality, even though you my be burning 10% fat at a high heart rate you are burning 800 calories (10%-800=80 cals of fat) at the low heart rate its more like 80% fat burned but only 100 calories (80%-100=80 cals fat) so you burn fat no matter what.

From a pure health perspective do a little of all, use the first 10 minutes as a warm-up(take it easy) then increase you workout intensity.  The best is to do what a re called intervals, 5 minutes fast, 5 minutes easy, do it for 5 sets, or any length that suits you, but mix it up so your routine isn't boring.