My first choice is a 270 weatherby mag. I love the velocity and it gives me the ability to up or down load. As others have suggested the 30-06 is widely popular here for the very same reason. The 300 mag class and 308 is incredibly popular as well. Big five; The majority of hunters here that chase bears either use a 300 mag class, 338 or the 375. One of the most popular calibers in Alaska is to 300 Winchester followed by the 338. The bear is not that hard of a animal to kill but it is generally considered critical to knock the beast down by breaking his shoulder with the first shot. Myself I have seen a average size blackie stop a 300 Winchester with a Nosler cold in the shoulder. It did break the bruins shoulder but I expect you would have to see how fast a 3 legged bear can run to believe it. For grizz I would choose the 375 for cost and recoil considerations. The smallest flinch on the bench is multiplied by 10x in the field plus excitement. Their have however been accounts of a Brownie being dropped with a single .22 lr in a emergency. Not my cup of tea though

We often see the charging beast scenario on the forums. I can only wonder what good any caliber might be at that point. Not arguing that bigger won't be better but at 20 paces with a charging angry buff will even the biggest save your hide ??