Didn't Jack Oconnor kill some mountain grizzlies with his beloved 270 pea shooter ?. Now a mountain grizzly may be in the 500 lb range but it is not to be confused with the slightly larger Kodiak bear. I would think that if they are on the menu you need to up gun with 338 being the minimum in my book. I have a friend in Colorado though that has shot probably 6 of them he has 2 mounted fullsize standing in his house all taken with a 300 win mag ..That bear is not something you want to see at 20 yards and have to wonder if your rifle is up to it or not. This is not flyfishing with catch and release ..your a@@ is on the line with a stupid mistake. You better make sure you can hit what your aiming at as well under pressure. Now other then the guy I know and one other not too many people that can spend the kind of money it takes to kill a Brown Bear so I would think a 300 WSM or WIn mag would be all one would need for anything.