if i shoot a ballistic gelatin block with a .270, a .30-06, and an 8mm mauser.. you will find that the wider, fatter bullet will expand to a greter diameter, and cut a slightly wider hole. the bullet designs are the same, often the velocities are the same. a longer narrower bullet will often have a higher ballistic coeficient- which means it is more efficient going through the air- and keeps its velocity better. A 150gr .27 or .28 caliber bullet of similar design will have a higher BC than 150gr .30 or .32 (like the 8mm).. and thus will keep its velocity longer. In spite of these differences- as long as you are shooting something in the .30-06 class of cartridges- there is not a deer of elk that can live on the difference between a .270, a .280, a .30-06, etc.. once you are in this class of power- and are using decent bullets- and can place them- the differences are pretty small.
Someone mentioned Bell shoting elephants with the 7x57, but that is a little different- as he was shooting about a 173gr roundnose full metal jacket.. and the one of the first things he did when he got to africa was pay someone to cut an elephant skull in half- so he knew exactly where that volleyball sized brain was. He knew that a smallbore heavy for caliber hardnosed bullets penetrated enough to kill about anything- with less recoil, etc than the big calibers- as long as they were placed properly. (but thats a bot of an aside from out discussion of deer and elk bullets-unless you are going to start head shooting them with FMJ)
