Fisherman killed a brown bear on the Kenai a few years ago with a 9mm. Not my choice at all, but if a 9 will do it, a 357 properly loaded will as well.
A strong 357 will push a 180 gr 1200 fps from a 4" barrel, and that'll penetrate the skull of any bear. As with any gun, you have to make the shot count.
Just remember, 95% of the people who give advice on bear guns have never even seen a grizzly or brown in the wild, under 1% of those giving advice have been uncomfortably close to one in the wild, and 0.00001% have had a DLP event.
If I remember right that guy lucked up and caught the spine and put the bear down.
Whatever a 7x57 can do a 270 can do better.
True fair chase is you in the woods buttnaked with nothing but your finger nails and teeth.
If you'e fixin' to put a hole in something, make it a hole to remember.
