What do you mean by 'how long the calories last'? A Calorie is a Calorie. Doesn't matter where you get it from, it's the exact same amount of energy. Fats do have a higher energy density than other macronutrients (9kcal/g vs 4kcal/g for carbs and protein), meaning that you get more calories from 1g of fat than 1g of carbohydrates. So 10g of fats will, obviously, give you more energy than 10g of carbohydrates.
If you're talking about satiety, then there is ample evidence that protein is much more effective than fats or carbohydrates in that regard: http://www.ncbi.nlm.nih.gov/pubmed/18469287.
If you're talking about satiety, then there is ample evidence that protein is much more effective than fats or carbohydrates in that regard: http://www.ncbi.nlm.nih.gov/pubmed/18469287.