Bottom line: .308 Winchester kills Moose dead. I have also witnessed it firsthand and via Canadian friends. Mostly, the hunters were using older 180 gr and 200 gr Winchester Silvertips and a few using older Federal 165gr TBBCs. Shots from 50 yards to about 200 yards. One Moose was simply shot in the head for meat, the remaining in the heart/lungs or even spine and then heart/lungs.

I'd recommend heart/lungs first shot.