When a bullet exits any animal, it means that some of the energy of that bullet hasn't been used, or dumped, in that animal. An expanding bullet, as against a fmj which is not designed to expand, creates a bigger surface area as it expands, dumping more energy, and at the same time crushing and tearing body tissue and bones.
This will generally result in greater shock to the animal, and more likelihood of death if the bullet doesn't hit the brain/heart/lung area.