While I've always heard that grizzlies don't eat humans, in the US, wasn't there a case of a nutty photographer and his wife (antigun, I gather) who got eaten in Alaska? I've also heard that Asian bears eat humans rather often?
And there are several cases where brown bears will actually eat humans. Most of these can be traced to being an old boar that has been injured and forced to live through other means down the food chain.
I would definitely go with the 870 using 3" slugs. I think it'd be easier to point and shoot with in a defensive situation.
But, I wouldn't feel under-gunned with the .30-06.
Both cartridges have about the same energy at 25 yards. I would prefer a pump shotgun for reliability. Even if a pump shotgun is stuffed full of ice you can clear the ice by whacking the forestock on your hand. Even if the bear is old and crippled it wants to kill me. I want something that is going to go bang.
Nothing in the affairs of men is worthy of great anxiety - Plato