The BC on 7mm projectiles give the 7-08 the edge after 350 yards or so.
BC is better on many .277 caliber bullets of the same weight as a 7mm when it comes to hunting bullets. Like the 140 grain AB BC is .496 in .277 and a BC of .485 in .284 caliber. This difference in BC is splitting of a pretty fine frogs hair of course. Most of the time this is avoided by not offering the same weights in these two calibers or shifting the position of the Ogive to affect BC. That doesn't change the fact that there are more than enough .277 bullets out there for hunting that have a higher BC than the .284 counterpart.
So the theory that the ballistis edge goes to the 7-08 just because it is a 7mm for hunting doesn't really hold water. If a person chooses bullets properly no edge is lost to a 7mm-08 when shooting a .270 Win for hunting situations. Now when it comes to match and target bullets there is no question as to which one offers the best BC's.
