Take a brown bear with a .348? I'd be more comfortable with the .375.
I have a classmate who hunts in Africa. Owns inherited fine double rifles. But his `bread & butter' rifle is a pre-64 Model 70 in .375 H&H. Works on everything up to and including buffalo. The `30-30' of Africa.
BTW, I fired his .375 with reduced `Cream of Wheat' loads, then full factory loads. Not that bad.
Dad was going to do the business with the .375. And you're right, that's the bread and butter rifle in Africa, although it's too much for almost any North American game.