"Recoil energy" will be equal for any two loads that have equal momentum (of bullet and powder gases) not ME. Equal momentun divided by the fixed weight of the gun give equal recoil velocity and therefore equal energy.

Personally, I've never put much stock in recoil calculators, because they don't reflect reality. Guns aren't free recoiling. As soon as it starts moving rearward it begins compressing muscle tissue and then moving the shooter. The huge additional mass (relative to the weight of the rifle) of your upper body radically reduces the gun/body velocity from what the calculations show. Since the recoil energy varies with the square of velocity, the exponentially reduces the energy. Intuitively we know this because it's the reason we hold rifles tightly to our shoulder lest you get clobered.

About the only way to make the formulas valid would be to suspend the rifle from a wire and stand a few feet behind it such that it strikes your shoulder just as the powder gasses and bullet exits the barrel and it is at that theoretical "recoil velocity". I'm not volunteering for that!

Bob