If all other factors are equal, the larger diameter and heavier projectile will retain more energy downrange and will impart more energy to the deer due to the larger frontal area.

But the point is, what do you need to kill a deer? If the newer 20 ga ammo has enough juice to get the job done at the range you intend to shoot, then it can be a BETTER choice. That's because all other factors aren't equal, like the size/weight of the gun for one, and recoil for another. I think it was a Federal ad that I saw, their 20 Ga ammo had plenty of energy out to 200 for deer. If a guy can shoot that far accurately, there's no reason not to shoot deer at that distance. The new 20 Ga ammo is much better than the old 20 ga Foster style slug.