I have been a big fan of 6.5mm cartridges for a long while now. Bought my first a 6.5x55 in the 90's. Bought a 260 rem around 2000 some time own a 6.5x284 and 6.5-06. Both of your choices are capable of extreme accuracy on "average" one is not going to be any more accurate than the other 1/4 moa is 1/4moa.
If velocity is something meaningful for you the 260 rem, the 6.5cm are the same. The CM is truly a short action cartridge. The 260 rem is hampered by loading to 2.800 COAL with long 140 grain projectiles but still shoots very accurately at that length.
To your choice my selection would depend on what frame I was going to shoot it on or if I truly wanted a short action. If I was not concerned about action length then all that is left is what type of firearm.
If I were to purchase a Sako 85S say I would be able to shoot and load rounds at 2.95 I would go with the 260 rem. The same circumstances for the 6.5CM if I were limited to 2.800 go with it. I would be interested to see what happens with the CM and small rifle primers. That would be a copy of the 6.5x47 mentioned.
Narrow your choice in firearm down and make your choice based on that you have plenty of .308 and 243 win brass really easy to resize.
You will have a really fine rifle with either choice. Always remember that velocity of any one of the choices mentioned you could obtain a slow rifle or a fast rifle. I had a modern action 6.5x55 that was slower than any and still own a 260 rem that's faster with better accuracy than my 6.5x284 which just likes it slow.
Good luck and shoot straight
Bob