There is a lot of biochemistry to this, see the textbooks for details (e.g. Lehninger or Stryer). I don't have the exact efficiency numbers at my fingertips but they don't seem to be the main thing. Fat has a much higher energy content than carbohydrates and is the preferred long-term fuel for most body tissues. However, the brain runs on glucose only, and on some weird stuff called ketone bodies in case of starvation. This is a reason for trying to have a balanced diet that has both fat and carbohydrates. In addition to the above, carbohydrates can be mobilized quickly and some energy can be extracted from them in the absence of oxygen (e.g. overworked muscle), whereas fat can only be used in the presence of oxygen. On top of this, glucose/carbohydrates can be converted into fat easily, but not the other way round. All together, "fats burn in the flame of carbohydrates" as Stryer puts it on p. 478 of the third edition...