Let me preface by saying I've not hunted bears, or shot a .338 - but I'd opt for 30-06 (I have owned one of those). It's as much gun as I'd care for, and I think as much as you need. Lots of grizzlies have been killed by 30-30; 30-06 ought to do. In fact... I think I'd hunt just about anything with a 30-06, and not feel undergunned. But then, I'm a whitetail hunter.