Its interesting to me that the .243 is touted as the answer for the novice big game hunter due to its low recoil, when the flip side of the problem is that the knowledge necessary to use the small round effectively on big game is greater than for larger moderate cartridges. From my point of view, the small bore is the expert's rifle, just as the big bore is, but for another reason. It takes time and effort to learn to use the big bore effectively, but over time the experienced rifleman becomes comfortable and competent with it. The light recoiling small bore requires no such acclimatization period, but its use on big game does require a knowledge of bullet construction, that too many novices and experienced hunters alike lack or disregard. There exists a broad range of suitable big game cartridges between these two extremes. Lets consider the following scenario . . .
Joe Moose Hunter goes into his local hardware store and pics up a box of .30/06 ammo for his long awaited moose hunt with his teenage son. His choices are either the 150 or 180 gr, loads, and the bullet construction of either weight is suitable for big game, and frankly his only concern is to ensure his box is marked .30/06; there seems to be so many different cartridges these days. Joe Jr. runs to the hardware store after school to pick up a box of ammo for his .243, making sure its marked .243 Winchester, not .243 WSSM. The lettering "70 grain bullets" holds no meaning for him. Dad doesn't notice the mistake, and perhaps doesn't know the difference between a varmint bullet and a big game bullet himself. If you asked him, he might say that they have to mark that on the box because the trajectories between the two loads differ.
The next morning finds the pair in their canoe, floating with the current, down a small meandering river. Some time later they round a bend in time to see a moose boil out of the water 75 yards ahead of them. Joe Jr. in the bow has been promised the first shot, which is now quartering away. He's on target quickly (Dad had made sure his scope was cranked down to a low magnification) his cross hair comes up centered in the space between the front legs, then rises half way through the body as he's been taught, and without hesitation he presses the trigger smartly. BANG! He cycles the action quickly, but has no follow-up shot. The moose showing no evidence of a hit, has disappeared into the willows and spruce. Dad didn't have a shot with Jr in front of him, besides he had his hands full lining the canoe up with the moose. Joe Jr. removes the live round from his chamber, reinserts it in the magazine, and closes the bolt, then helps paddle. They maneuver the canoe to where it can be pulled up on the river bank, and walk back to where the moose came out of the water. At first they find no blood or any other evidence of a hit, but then they spot drops on some willow leaves that are thick and dark red, consistent with a surface wound, there's more on some high grass, though smears not drops. They take up the trial, but an hour or so later they emerge from the spruce to a wide extent of muskeg with a flooded swamp beyond. The moose is gone, and they can go no further. Father and son head back to the river, with Jr's confidence badly shaken.
A .243 can be a giant killer, with the right bullet, with the right shot, and with the proper placement. But that's a lot of "what ifs", when proper placement is the only criteria for a game bullet fired from a 6.5X55 or 7X57 Mauser, or from a .260 or a 7-08 Remington. These rounds have the bullet construction, the bullet weight, and the impact velocity to ensure sufficient expansion and have the momentum necessary to penetrate through the foot and a half of game animal that is necessary with a quartering away shot, to produce a humane kill. If you're going to use a 6mm cartridge on a large species of big game, learn something about bullet construction, and doing some of your own testing to find out what your bullet won't do, is more important than assuming what it will.