I find myself agreeing with Brad above. If you need something more than a 30/06, get a .375. Somewhat lacking from this thread is why a medium is needed.

Most mediums, IMO, have very little to no advantage over 30/06 class cartridges today simply because of today's better bullets. I love the .338, as an example, but it simply isn't needed today. It came about as an answer to reliable terminal effects in the cup and core bullet era. Lighter calibers simply didn't work so well on larger game; now they do.

I'm separating need from want. If a person is filled with euphoria with the thought of a medium bore, I'm all for 'em. Get one. I just don't need one any more. But I do have a nice .375 H&H that they will put in my coffin with me!