I like to use the best controlled expansion bullet that works the best in that particular rifle.(accurate, functions in the mag)
I have used coreloks for years on moose and caribou not one has bounced off their hide. I'm not in brown bear country so I don't worry about it much. Grizzlies in the interior aren't more than 5-6 hundred pounds. Not many bigger than that (in the interior). If I did I would use one of the great new CE bullets that are available today. Accubonds, interbonds, TSX, TTSX weldcore, Kodiak bonded bullets ect. Many more.