Flip a coin.
For deer/antelope hunting the 243 is hard to beat. If you move on to elk then the 6.5 CM would be a better option.
Most 243s come with a 1:10 twist barrel so you're going to be limited to =/< 100 gr. bullets, but with deer size animals that is plenty.
My wife uses a 243 for her deer/antelope hunting. Tried the 87 gn Bergers VLD for hunting. They were too violent, leaving a rather large exit wound and lots of damage meat. We went to the Hornady 100 BTSP and they work better.
I normally use a 257 Roberts for deer and antelope. But this year I've been playing with the 6.5 CM. It works, but again it destroys a lot of meat. Overkill in my opinion. But in the Creedmoors defense, I've only used 140-143 weight bullets.
I'm going to save my 6.5 CM for elk and go back to my 257 Roberts for deer/antelope.
Again you wont go wrong with either the 243 or 6.5 CM.
Wife got this guy at 540 yards with her 243 last fall, using the 100 gr BTSPs.
I got this one on the first of this month with the 143 gr. Horn. 6.5 CM, at 651 yards.
They both work, flip a coin.