Why I even think it could have any effect: maybe when the body has deficit of the oxygen, the burning reaction modifies to burn more sugar/fat/whatever (i.e. instead of burning each molecule completely it is burning them just up to a certain point and go over to the next)? (have heard something like that but would like to have some solid facts :) If there is any difference, how much is it, is it worth to think about during workouts?
Quite simply, no. In order to understand why, you have to understand the metabolic pathways used in exercise. If there are slight differences in the amount of calories burned, it is due merely to the difference in energy needed to move the lungs.
Essentially, your muscles use Adenosine Triphosphate (ATP) to perform their work. The different metabolic pathways all result in generating ATP. The three major pathways are:
Only one of those pathways uses oxygen. It should be noted that the metabolic pathways are listed in order of the amount of Calories burned for that type of activity. While aerobic activity burns a higher percentage of fat during activity, the energy demands are fairly low and there is no "afterburn" associated with that activity. It should also be noted that the metabolic pathways are cumulative. You are still operating oxidatively even when you are predominantly operating in the glycolytic manner. The anaerobic pathways, while they burn more carbs immediately, they also require more Calories. When you finally come to rest, the body has to replenish the energy from somewhere. In the absence of food, this means the body has to burn fat to create glycogen--which is what the "afterburn" of high intensity interval training comes from.