Both chamberings will do the job on appropriate game when using the
right bullet.The 7x57, which is usually chambered in a longer action, can be loaded with heavier bullets without compromising powder space nearly as much. But, is there really a need for a heavier bullet? I'm loading my 7/08 with 140 gr Barnes TSX - at close to 2800 fps from a 22" barrel- using Varget. One such bullet passed the LENGTH of a sizable northern buck. The 6.5 lb, scoped and loaded, Kimber Montana is a joy to carry and gentle on my bad wing. Bigger isn't always better, neither is more. Sometimes, just enough is just about right.
