I prefer to pick a bullet and put a cartridge behind it, I really like what the 140 Berger does so I put a 6.5 Sherman or SS behind it, I really like the 165 Matrix and 170 berger so I put a 270 WSM or Sherman in a long action under it, I like the 177 Hammer so I put a 28 Nosler under it, 215 Berger gets a 308 to 30 Nosler and may be the most versatile bullet I've ever shot elk with. I really like the 250 Berger so I would put a 338 Sherman or a 338 RUM under it.
One thing I will not do is shoot a rifle that beats me or anyone using it, I've seen a good number of elk very, very cleanly killed inside 300 yard with a 223 because the shooter was confident behind it. I would have no problem shooting elk the rest of my life with a 6.5 Creedmore or 6.5x47L, I would not be happy being stuck with a large 338 for everything so for me it's a two gun solution, something in the 6.5-270 range and the BIG 300 or 338. In my area the most common guns are 243, 270 and 30-06 for elk, the only time I saw a magnum was dudes from out of state.