My thoughts would be to take them both out and see how they both shoot. Take the one you shoot the best and spend your time with that one. You say that you are going to the Southeast to hunt, but not exactly where. The farther south you go the smaller the body size is on the deer. This has to do with Core body temp in relation to the environment that the animal is in. Colder the environment, larger the core body must be to maintain the internal temp. Warmer the environment, smaller the body size.
Both the .243 and the .270 will do the job, but placement of the shot is everything. I have both calibers and have never had a problem with either one, both have knocked deer down extremely well. Use Speer 100 gr. in the .243, expands very well and has great knock-down. My last deer fell to that round at a lasered 252 yds, heart shot and just plain fell over. The .270 with 130 gr. Hornaday will also drop'em like a rock. Just hit the heart/lung area.
Mark