I just can't STAND to keep quiet anymore!
Dogger, take a look at the muzzle velocities of the different bullets you can use with these different calibers. Pay attention to sectional densities and ballistic coefficients. Think about trajectories.
In a previous post you seemed to lean toward .270 and .280, which is sensible enough, but then you mentioned .25-06 as an alternative. That was clear thinking!
There IS no better all-around cartridge than the .25-06 for all-around shooting in the lower 48 states. Think of it: the .25-06 can drive a 120-grain Partition at about 3100 fps. The BC is up around .390, and sectional density is .260.
As compared to say a .308 Winchester, with which a 165-grain bullet is about the heaviest you can drive with any ooomph, well...the .308 165-grain Partition has a sectional density of about .248, and the BC is about .410. The big difference is you will be able to drive the .308 bullet at about 2700 fps.
The .25-06 will shoot flatter, with less recoil. It will be practically as accurate, and you may well shoot it better because of the lessened recoil. And when you load it up with varmint weight bullets, look out! There is NO comparison between the .25-06 and the .308.
If there is any doubt that the .25-06 will take down an elk, well, the livingrooms of America are full of experts who say you have to have a .300 Mag to hunt elk, but the woods are full of hunters who take elk with calibers much smaller than that. It's all shot placement and bullet performance. If this were not so, then every early-American explorer and mountain man would have been eaten by grizzlies or some other critter or would have starved to death. And the Native Americans were nothing more than bear-feed with their bows and arrows. I guess the bows made good toothpicks for the bears.
When lighter, varmint weight bullets are the subject, well...the tables tell the story. The .25-06 is the obvious choice. The .308 can drive a 110-grainer at about 3300 fps. Not bad. The 30-caliber varmint bullet has a BC of about .200. The .25-06 will drive a 75-grainer at almost 3700 fps. BC will be about .200 for this weight bullet. Which do you think will shoot flatter?
There is no better all-around cartridge for the lower 48 than the .25-06. If you want a rifle exclusively for elk, then something larger may be a better selection, but for versatility, the .25-06 can't be beat!