308 enough for brown/polar bear?

I wanted to get a 375 H&H but at the time I didn't know how well I would be able to shoot it. When I finally got to shoot one heck it seemed easier than my 45-70 with hot loads lol.
My .45-70 might be too long for bear defense.
Winchester 1886 .45-70 lever action.jpg
 
While a "battle rifle" would be a comfort in a bear attack I would think it would interfere with other activities. I one is hunting you would have a supposedly adequate rifle in your hands. If fishing, camping, cleaning a downed animal a .308 large capacity rifle is awkward. You are the only one who has to be comfortable with whatever you decide. If the worst happens and you were correct you get to brag if you were wrong we get to read about it.
 
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