there are really just 3 or 4 considerations
6mm has significantly less recoil and is easier to see your own trace
6mm can be pushed (in popular short action non-magnum cartridges) fast enough that it is within a tenth of the 6.5mm dope also comparing short action non-magnums. i.e. it makes up in velocity what it loses in BC
6mm has significantly less umph, kicks up less dirt when you miss, moves targets less when you hit and every match there is someone complaining about getting a hit on a 1000+ yard target that the ROs didn't see with a 6mm. this is only a consideration for steel, not paper or electronic targets if that's your game
6.5mm has significantly better barrel life. roughly 2x. if you figure a barrel costs $600, then you're looking at 20 cents a shot for 6.5 vs 40 cents a shot for 6mm, give or take, just in the cost of steel and gunsmithing, not counting ammo components. of course, you can push the 6mm slower and get better barrel life.