My slight of build wife, and both my boys at the age of 12 cut their teeth on the 260 Remington youth model M77 Ruger. 10 dead critters later they all still love it. All kills were mule deer and pronghorn but upon postmortem inspection of lethality, I would have no reservations using it on an elk with the right load and bullet. We have been using handloaded 100gr Barnes X and they are tremendous performers.
The 7mm-08 may have an ever so slight advantage (100 fps) pushing the larger 140gr bullets but the effectiveness of the 260 for flatter shooting with lighter bullets is tough to beat for the light recoil it produces. They never remember the recoil on live game anyway. Train with an identical M77 in a lighter caliber or rimfire and develop technique and shoot the centerfire sparingly in the early stages of development.
The 7mm-08 may have an ever so slight advantage (100 fps) pushing the larger 140gr bullets but the effectiveness of the 260 for flatter shooting with lighter bullets is tough to beat for the light recoil it produces. They never remember the recoil on live game anyway. Train with an identical M77 in a lighter caliber or rimfire and develop technique and shoot the centerfire sparingly in the early stages of development.