I have a buddy who has taken more than a dozen elk, some really BIG ones, with a .243 shooting 87gr HPBTs. Add to that more than 100 deer and several caribou, and I think you get the picture. The .243 is the only rifle he's ever owned, and he says that it's not the caliber, it's the hunters ability to place the shot that is the deciding factor.
Same with your .243 and deer. I think the real question is how far can you shoot your rifle and hit a pie plate with the first shot under field conditions?
