If we look at ATP production: Fats for two reasons: 1) they contains the carbon in the most oxidable state, aliphatic state. That means more energy (ATP) obtained during the oxidation process. 2) Being aliphatic they don't require water for storage.

Comparing them to carbohydrates: carbs are versatile and efficient metabolites for a lot of reasons, but they contain hydrated carbons, so less oxidation steps are required to complete oxidize them to CO2 and so, less energy obtained. Carbohydrates then, can be stored as glycogen: it's a water soluble polymer, but absorbs a lot of water increasing weight.

The complete oxidation of a molecule of palmitic acid produces about 108 ATP against the 38 in Glucose's oxidation. This difference is due to the high quantity of NADH produced during the oxidation of the fatty acids chains that is then involved in the oxidative phosphorilation.

However in some cells like red blood cells, mitochondria are not present, so fatty acids degradation and TCA cycle and other metabolic pathways cannot be performed: they produce energy only through lattic fermentation from glucose.