It is not just mass. Hollow points are considered to have more stopping power because they mushroom to a greater diameter and impart more energy to the target. A steel round of greater mass can pass through the target with greater ease imparting much less energy.

For shot the problem is that each piece is very small, so air resistance slows it down meaningfully if the density isn't there (e.g. steel vs lead); so the exact same power at the muzzle will have very different power when hitting the bird if a less dense material is used.