Not in the slightest. Check out glycemic index [0]. Sugar absorption rates affect how your body functions. There is massive negative effects when your body is working hard to balance your glucose levels due to sugar rich foods or high glycemic index.
Your body does not work harder just because the food has high glycemic index, I would say it is the opposite. The body has a very easy time using glucose for example compared to fructose which needs to through the liver which in turn increases the risk of liver damage if you eat too much.
However I was obviously referring to the weight gain and loss I mentioned in my previous sentence. I.e. the long distance runners in your link that chooses high glycemic food are not getting fat anytime soon.
The point you are missing is that with one diet you would out of control crave far more calories. While on a different diet you would have to force yourself to eat beyond feeling satisfied to reach the same number of calories.
I'm not missing that, it was just not something that was discussed. I was talking about weight gain and weight loss, not how easy or difficult it is in practice.
What you eat will of course matter when it comes to nutrition, muscle gain, satiety and many other factors but that in itself does not generally remove that a calorie is a calorie (unless extreme diets).
You asked why it makes a significant difference. And it looks like you answered your own question. A calorie being a calorie is one of the less interesting factors when it comes to actual practice. And yet it gets repeated ad nauseum every time the discussion comes up.
Over the long haul, no it's not. They all have different levels of nutrients, vitamins, minerals, carbs, fats, and proteins. Please try eating 2000 calories of sugar a day and nothing else for a while and see how long it is before you puke your guts out.
Eating 2000 kcal of vegetables is the same as eating 2000 kcal of bread and meat.