If you put a good 100 gr. .243/6MM bullet into the kill zone of ANY Whitetail Deer out to 300 yards, it is a dead deer! It is unexplainable, but I have even seen better blood trails from the .243 than some other calibers at times!
The theory that Flags mentioned makes great sense, as a heart shot deer can run 200 yards or DRT.
There are only two DRT shots, brain or spine, (neither of which, I would recommend!)
A double shoulder shot will put a deer on the ground quick, but ruins a lot of meat!
Of the two calibers you mentioned, unless the majority of your shots are <100 yards, I'd pick the .243 all day long and twice on Sunday!