Well moose seem to be "low strung"
I have killed 4. 3 were not impressed with my rifles. 2 were killed with a 375H&H and one with a 348 Winchester, and one with a 62 caliber flintlock.

The 3 I killed with the breach-loaders seemed to be disinterested in my guns and me. One was hit with my 375 at only about 130 yards and it didn't even seem to notice my efforts. So his 308 may not be "too small" and it's not if the bullet gave him an exit. My experience with 3 of the 4 moose I killed is that even a 375 H&H doesn't get a lot of reaction from them. They didn't stay on their feet for very long. Maybe 7-10 seconds. But they just don't seem to feel any pain of even any disturbance.
I have family in Alaska and they have killed dozens of moose. The tell me that my experience is pretty common.

The one I killed with the flintlock was the only one that dropped at the shot (halfway) The chest hit the ground at the shot and the real legs splayed, stood for a few seconds like a big A-Frame and then fell. But within about 3 seconds it fell over and that was the end of the drama.