Arrows use a different mechanism to kill game than bullets do. An arrow penetrates into the chest and every time the animal moves that arrow shaft whips back and forth causing the broadhead to continue cutting the internal organs to ribbons, providing the arrow doesn't exit. The blood trail from an arrowed animal is pretty impressive.
Once a bullet has come to the end of it's trajectory, the wound tends to be large in diameter, relative to the bullet diameter, its depth though is dependent on momentum relative to the expanded diameter. The wound has liquified tissue and pulverized bone, but no more damage is done after the passage of the bullet.
The nature the bow requires that a game animal be shot from relatively close range, yet how do most folks set up their .243s? Mostly the barrels are long and the scopes large, in other words these things are equipped to take advantage of the wonderfully flat trajectory; they're ready for the long shot. Mine is no exception having a 22" medium contour varmint barrel and a 4-12X scope. Modern bullets have made the fast moving small bores more effective on larger game, but that doesn't make a .243 an elk gun any more than it makes it an elephant gun. Sure you can be successful if you shoot from short range, and are able to place your bullet with micrometer precision, but that's not what defines a big game rifle to me. To me a general purpose big game rifle should have a reasonable expectation of killing a big game animal with a single shot from any direction or angle within the range limitations of the hunter and/or his rifle. Even those who champion the use of the .243 on large game admit it does not meet this criteria. If you want a high velocity small bore with light recoil for general purpose big game hunting, the .270 is a much better contender.