Barrel life, and possibly energy depending on variables.
The CM is basically the .260 Rem, slightly shorter case/shoulder. The .260 Rem is a necked-down .308, to 6.5
The 7-08 (one of my LR favorites) is the .308 necked down to 7mm.

Simple rule...the more you neck down a case, the shorter your barrel life. No free lunches here. Forcing the same amount of burning gases and plasma through a smaller tube increases erosion of the throat.

Despite all the sexy names and marketing hype of the cartridges du jour, the .308 remains a solid choice for many. But if you feel you need the extra bit of flat-shooting provided, the 6.5's (and the 7) will give an edge.

FWIW, the 6 Creedmoor, is just another incarnation of the .243- a whitetail standard for many decades.

But, you didn't say what game, and what distances- important considerations in making a recommendation. Unlike steel and paper, energy at the target matters in a hunting application.