I too am shopping a "new" caliber. I am leaning towards the .308 myself. I will use it on Lopes, Deer, Elk, Bear ( given the opportunity). Here's why . . . First of all, it is the most popular round for bench shooters. My first criteria is the rounds ability to drive tacks! Second is killing power. According to several articles, a round should have at least 1500 pounds of "Energy in Foot Pounds " to ethically take down an elk sized animal. According to the Federal website a 180gr. '06 and .308 round are only 2 hundred FP's difference at 300 yards! 1865 & 1672 respectly.
Also, there are lots of ammo choices for the .308 if you don't roll your own like me. Yes there are more '06, but still plenty for the .308!
Lastly, and maybe most importantly . . . I'm tired of beating myself up at the range with magnum this or that. First rule in good shooting is you have to practice, practice, practice! Pounding your shoulder makes your shots go afoul. Mine anyway. So the .308, with 17.5 pounds of recoil energy and the '06's 20.3 pounds, less is more in my opinion.
Bottom line, a well placed .22 will kill an elk . . . 10 feet away! So all these guns will do the job.
My conclusion: I am willing to shoot a lighter round at shorter distances (300 & under) in order to shoot more, shoot better, shoot ethically, and save my shoulder. After all, the military can't be wrong when they preferred the .308 for their sniper round (as well as bench shooters) for so many years.
Oh, the .35 . . . Federal only shows ONE round offered for that gun, , , sell it.