It may not take much to kill them, but they are big. Personally I would not consider a 243 for anything bigger than deer unless it was cow elk up close.
I have killed 3 Shiras moose. First one was front on a bull shot with 338, dropped on the spot, bullet did not exit. Second one was a cow at about 40 yards, one 338 through the chest appeared to be a miss (it wasn't), I put a 2nd bullet through the chest which didn't appear to faze it, it just kept walking, third shot also in the chest didn't change its pace any. It went about 50 yards before going down. Third moose, also a cow, took a 375 taylor through the shoulder broadside, did not flinch, a second 375 about 4" to the rear of the first shot put it down.
My belief is that if you NEVER miss your exact point of aim and always have a good shot angle, a smaller round is just fine on big animals. However, I hunt in the real world where animals do not always cooperate, vegetation that you didn't see before the shot suddenly appears, and where shooting positions are not always rock solid.