The M1A/M-14 has more than enough energy to kill any North American game, with proper distance and shot placement. BC (Canada) regs for Bison (much tougher than elk) states:
7. ammunition to hunt bison must be constructed with a 175 grain or larger bullet, which retains 2,712 joules (2,000 ft lbs) or more energy at 100 m.
My 20" Savage PC .308 with Barnes 175 LRX @ 2655 fps has over 2000 ft/lbs at 200M and still has over 1100 at 600M (more than enough for deer). With over 1550 ft/lbs at 400M, a .308 is a great all around North American big game cartridge. Considering compound bow hunters are killing the largest game with 50-80ft/lbs [yeah, yeah, I know it's a little different but c'mon] I don't think there should be any problem taking elk/moose with an M1A/M-14. I hunted with one last year (got skunked) and the only downside was weight. With the new Blackfeather stock at www.M14.ca
even weight won't be an issue. I handload with IMR 8208 XBR or IMR 4895 and have no problem. Also, with a semi-auto .308, you have a great self-defense weapon against even the largest brown bears.