Theoretically there isn't any difference at that range other than recoil, 6.5 CM splits the difference between 243 and 308. But the 308 doesn't offer a single advantage at that range while the 6.5 has all the advantages if you ever decide to start shooting really long.
And while admittedly a small sample I've had the opportunity to shoot 5 different rifles in 6.5 CM. Every single one of them was more accurate than any 308 I've ever fired. But not by much. I'm not saying every 6.5 is more accurate than every 308. Maybe I've just been lucky buying factory loads and working up handloads
