Oh,
I thought we were talking about the diameter of the hole, not the energy delivered by a heavier slug.
Care to address the diameter part? Compare a 150 grain .270 to a 150 grain .30-06 to keep bullet weight constant.
In that situation the 30-06 would deliver more energy closer. The greater surface area of the bullet allows for greater transfer of the energy to the animal. If the bullet is narrower and, say, escapes the body of the animal, that energy is wasted beyond the animal. The greater surface area (20%) slows the bullet down in the animal more by transferring its energy to the animal.
Additionally, it will create a slightly larger wound channel which may nick a vital organ which could have otherwise been missed.
That said, the 270 bullet may have a better balistic co-efficient at the same weight but quality bullets generally eliminate that.
The flip side is that the 270's lesser surface area will allow it to travel further and flatter while losing less energy to wind resistance. Beyond 250 yards, it will deliver more energy to the animal simply because there is more energy left with the bullet.