If you look into the competition realm, the 308 died at the hands of the of the 6.5. Now i'm starting to notice (not that I pay a lot of attention to it) a good number of 6mm's running the course.
Why? Speed. A 243 can get a lot closer to the "usual" limit of 3150fps for match use. Speed makes a flat trajectory, a flat trajectory it easier on the end user when a distant target is misjudged.
Why use a 6.5? More energy means a close miss at ELR distance is usually easier to spot. A larger bore to case capacity mean the throat is going to last longer. The 6.5 is known to have excellent BC which is going to buck the wind better when velocity starts to drop.
If you ever decide to take your new rig hunting, the 6.5 will give you a little more room for error. Having said that, i've killed more critters with a lowly .243 than most of my rifles combined; it's the indian, not the arrow.
I have both & love them dearly. For my preference, I rock my Creedmoor most of the time. In the grand scheme of things, you cannot go wrong either way.
t