Never send a boy to do a man's job!! Ifin' the animal your hunting needs that kind of power to take out there's no use in going smaller..why oh why do we need this, how about the .416..much better than both!
I picked 300. I have one and love it. It will do all that i'll ever need. Mine is RMEF edt.700 Rem. SS Mag Na Port-ed and an R-3 recoil pad topped off with 3x9x40 Zeiss. It'll shoot like an 06 re-coil with what i had done to it. Sorry i got carried away but i'm proud of it, and it cost more then any gun I've owned. Lost my mind one time but glad i did it was almost for my 50th. birthday, thought it would be my last gun HA HAAA HAAAA...later
The 300 Rum is too much powder for a 30 cal. The 338 can use that space.
But as Dash 6 says, if you are going to take that much recoil, you really should have a heavier larger bullet, like the 416 mag...that is why I have both. For hunting anything over 800 pounds and under 350 yards, I'd rather have my 416.
My 300 Rum makes an adequate 500+ yard whittail gun.
I don't get into magnums. Living here in the east I can't enjoy them. I go on the 'Fire and talk and those guys out west are shooting their magnums at 600 yard targets and steel rams. Now that's what I call enjoying a magnum. If I lived out west I'd be all about magnums because I could shoot and enjoy them. As it stands now the range I belong to has a 100 yard backstop as it's long range target. There is another range near me that goes out to 200. I can't enjoy magnum ownership on a 200 yard range. If I had somewhere where I could shoot at least 500 yards I'd be really into magnums. Where I shoot I might as well just have a .300 Savage.