Ditto on Mr. White.
Hatterasurf--Mr. White has hit the nail on the head (or the whitetail in the CNS, take yr pick)--The larger cartridges simply give you a greater margin for error under less-than-perfect conditions.
Now, I'm not OK'ing shooting at a running deer, nor taking "iffy" shots of 250 yds from offhand, or anything of the sort. Just the usual cold, rainy, sleepy, deer-jumped-just-as-I-pulled-the-trigger, deer-stopped-behind-a-tree, Murphy's Law went into overdrive, sort of things that go into a normal hunting trip.
Also, some hunters--present company excepted, of course--are less than well-practiced shooters. This is not the best situation, but it IS true. They can hit the soccer ball-sized chest of a large whitetail, usually, but certainly not with any precision.
And in all those cases, the larger bullet, and larger wound channel, give you a little leg up.
If you're willing to PRACTICE with it, regularly, and know your deer anatomy well, and are sportsman enough to pass up "iffy" shots, the .243 will work just fine.