I like the M14, but I would not want to carry it up and down mountains. The newer AR type platforms are made of light weight aluminum alloys that shed a lot of weight, as well as the availability of parts. We dead-lined two M14’s in Iraq and did not get them repaired until we had returned CONUS, something to do with NSN and parts ordering issues.
Unless I am getting some really long range out of it, I would opt for a 5.56 rifle. If I have to pack the extra weight, it had better damn well reach out and touch. IMO 7.62 doesn’t give that much more of an advantage over 5.56, not enough to cause me to carry twice the weight. Now going back to the topic of 300WM/338 then yeah, now we are talking. But for a general purpose rifle or DMR type (0 to 600) I will take 5.56, especially if I have to maneuver in mountainous terrain.
Something else to keep in mind is the ballistic effects in high angle fire as it applies in mountainous terrain. An enemy target may be 800 yards out, but if the angle is extreme, you could be shooting him with the ballistic effects of a 300 yard shot.