Times sure have changed. I had a Grandfather who killed moose for decades with a .32-40. His brother 'hated the recoil', so he used a .25-20. My own father upgraded to a "big" rifle...a .38-55...and also killed moose for decades. I saw him kill a cow & calf with two shots on many occasions. None of them ever owned a scope in their lives, and I suffered huge amounts of 'city slicker' ridicule when, in the early '60s, I put a 4x Weaver on my 'meat wrecker' .30-06.
Both of them used a technique rarely seen these days - they stalked. First they found a moose; then they spent whatever time was necessary to get close enough to place one careful bullet where it killed the moose quickly and effectively, without ruining any edible portions.
Moose hunting with a .308 & 220 gr. RN bullets wouldn't worry me one bit. But I'd stalk instead of standing off 400 yards lobbing rounds at it.