The .243 is a great LITTLE round. I've used it on many deer, and even my biggest. But the biggest whitetail is altogether different than a small elk, or medium elk, or avearage bear.
I believe I could kill all these larger animals with a .243 but would opt for my 30/06 or my 8mm/06 first. I don't really own a great elk rifle, but sure wouldn't select my .243 from my rack if offered a hunt.