I have used from the 45/70,loaded down 458Win) on down to the 270Win for moose. They all went down, after awhile. The 270Win is not that much more of a cartridge than the 7/08, when looking at the energy columns. I used both the 130gr and the 150 gr in the 270 on moose. In the 270 I used the bullet weight that shot the best in that particular rifle. I should add two things. These were the eastern canadian moose, and not the giant alaskan models, although I am fairly sure they live and die by the same rules. With the exception of one neck shot with a 300Win Mag 180 gr Silvertip, they all took a while to fall over. Kind of an anxious moment. On my first one, my buddy told me "do not shoot again, he is dead". He was right. My 458 loaded with the Rem 405 gr double cannular bullet at 2000fps did not do any better with a chest shot. Farthest shot was "about" 180 paces. In the areas that I was hunting, Newfoundland, you could normally get closer. Shortest was 9ft. on a sleeping bull, with a 500gr lead 45 cal in the head. Even that one thrashed and vibrated for about 5 seconds or so. I took off as I thought I had just grazed him and he was going to get up and be mad,my young and dumb years).
My hunting partner, during those years, used a Husqvarna bolt gun, with iron sights, chambered for 308 Winchester and 180gr Silvertip bullets. He shot more moose than I did and never had one "wander off". He used to kid me about always changing rifles. He probably was right.
Yes, a moose looks huge. But if think of his legs as being only half as long he is a much smaller animal. I think the 7/08 will do fine, with a 160 or 175gr QUALITY bullet. Like anything else, bullet placement is the key. Even with the biggest magnum, if you cannot get the shot you want, don't take it.
Carl L.