In KY, a caliber restriction exists on elk and bear hunting...rifle hunters must use a minimum of a .270 Winchester...(.243s are not allowed)
A deer (whitetail or mule deer) is not really hard to kill (not necessarily DRT)...and a .243 bullet through the lungs will kill as well as any other caliber...
The advantage of a 7mm (.284) bullet is in its sectional density, which tends to be "heavy" for caliber...and thus generally gives better penetration for shoulder shots or hard angle shots...
Elk/Moose are bigger and tougher, and while a .243 bullet through the lungs will equal a dead elk/moose, the problem is getting the bullet through all of the muscle and/or bone to the lungs...