I think you also need to consider the loss of energy of a bullet exiting the animal. A smaller diameter bullet with a certain amount of energy is much more likely to punch straight through tissue and carry energy with it than a bullet of a larger diameter with the same energy. The larger bullet is going to shed a lot more of its energy into the tissue before it exits. The 22 bullet will most likely go right through with little loss of energy (unless it hits a bone and becomes a ping-pong ball) than the 44. Its the energy absorbed by the tissues that knocks the animal down or makes for the quick kill from massive hemorrhage. A 243 hit right below the spine will probably still allow the animal to run off. A 44 hit right below the spine will still immidiately incapacitate the animal.