For a stalking rifle, it seems to me that that a shot could present its shot opportunity pretty quickly and maybe not at the best shot angle. Yes, use enough gun and both the .270 and the H&H with the right bullets are enough for the stalkable stuff that I know about aside from the big bears in North America. That brings us to the recoil of that H&H magnum verses the .270 on an iron sighted rifle. Recoil is the reason that I built up a 7mm-08 instead of using my 7mm RM for my whitetail deer hunting. Shots can happen fast and at odd angles and a perfect cheek and stock to shoulder position favored that lighter recoiling cartridge.
