I would say that it is most of the time pretty close.
When you are going forward at a sustain speed, you basically have three things to fight :
- The rolling resistance of your tyre.
- The aero resistance.
- The incline resistance.
None of those is linked to the crank length, so you basically need to put the same amount of power with any crank choice.
When pedaling, the amount of power that goes to the wheel is :
- P = F.S (P : Power in Watt, F : Force on the pedal in Newton, S : Speed of the pedal in meter/second)
The speed of your foot (or the pedal) is :
- S = L.2.π.c (S : pedal speed in meter/second, L : crank length in meter, c : cadence in /second)
As said previously, at any given speed, P is constant for any crank choice, as is c, we then get :
- P = F.S = F.L.2.π.c <=> F = P/S = P/L/2.π/c = P/(2.π.c)/L
Since P/(2.π.c) is not linked to the crank length, to use shorter cranks, you will have to put more force on your feet, but they will go slower, so in term of calorie, there should be basically no difference at rather slow speeds. You might damage more muscle fibers with shorter cranks, which might cause more aches afterwards.
However, at higher speeds, there is one thing that will accelerate with every pedal thrust : your legs. If you do a bigger circle with your feet, your legs will move more, and accelerate faster. And that is also power consumption. This means that at higher speeds, using longer cranks will consume more calorie.
What I just said, is only valid in a perfect world. In the real world, there are perturbations, which will lead you to get imbalances you will have to correct. Those will take longer to correct on shorter cranks, which means more calories consumed (calorie = power x time). So shorter cranks, especially if not perfectly mastered or at lower speeds will consume more calories.
So in the end, shorter cranks should consume less energy than long cranks at high speeds, and longer cranks are better at low speeds or when going uphill or on uneven terrains.
Short cranks will also cause more muscle fiber destruction which means more aches afterward, especially at low speeds or when going uphill.