There is no need for both. Anything you can do with one, you can do with the other. In 1925 they were loaded much differently, but with todays modern loadings a 30-06 150 gr bullet @ 3100 fps is so close to 270 trajectory to not matter. A quality 150 gr 270 bullet is every bit as deadly on larger game as a 180 gr 30-06 bullet.
I could use 3 cartridges to hunt anything on the planet.
I'd choose 223 for everything up to and including deer. It still wouldn't be my 1st choice for deer, but under the right conditions I'd use it.
For big stuff that bites back, 375 magnum.
It is for everything else that it gets difficult. The truth is that everything from 260 up to the 338 magnums is really designed for the same game. For stuff that bites back the 338 is still borderline and wouldn't be my choice and the 260 and everything else in between works just fine on elk size game. I say pick the one that suits you fancy. I'd probably use a 308, but there are no bad choices here. Just personal preferences.