While I have never hunted large dangerous game, I base my opinion on the best rifle for you would be the one you shoot best. I'm not talking off of the bench, I'm talking from actual field/hunting positions, and a rifle you can make a fast follow up shot with. Now, if you don't have either caliber and are planning on buying one, I would say either one will fit the bill. Personally, I would get the 338 over the 300 Rem Ultra Mag, mainly because I don't like Remington 700s.