Here's my take on the whole matter. Sure you can get away with a light recoiling .30 cal gun on dangerous game with proper shot placement. Heck, a whole bunch of elephants and cape buffalo have fallen to 30-06's. However, I sure wouldn't take one on a cape buffalo hunt, and I wouldn't take one on a grizz or moose hunt either. I'm a pretty experienced hunter and a fair field shot, and that experience tells me that sometimes even the best of us make errors that lead to less than perfect shot placement on big game animals. I've also seen alot of animals punched right through the boiler room run 2-400yds. Those things lead me to believe that I owe it to myself and the animal to use a firearm that is IDEALLY suited to the game and conditions I'm hunting in, not just barely enough to get by. And if that goes for me, it sure goes for the little misses too, especially if she's not as experienced or as good of a marksman as I am.
On that note I'd say no less than a 8mm/.338 on grizz and moose. If recoil is a problem, solve it with a good recoil pad and a brake, not by using a lesser cartridge. I haven't shot the .338 Fed or .325WSM yet but I've heard they are fairly tame in recoil for the ballistics they offer.