6CM is basically a new version of the .243Win. But, most have a better twist rate in factory rifles to push the heavier bullets.
If you are building one, flip a coin. But, 6CM has better brass options available, even though Lapua makes both, and would be my choice.
6.5CM can use heavier bullets, but at much lower velocities. For deer or antelope, it is basically a wash. I would run a 130 in a 6.5CM myself. And a 105 in a 6CM.
I just got back from a NM pronghorn hunt a few weeks ago.
My daughter used her 6.5SLR (similar to 6.5CM w. 130 OTM @ 2888fps from 22" barrel). 391 yards, buck never even moved after the shot. Exit hole was about silver dollar size. Lungs were Jell-o.
I shot mine with a 6CM (105 Hyb @ 3101fps from 24" barrel). 445 yards, buck dropped at the shot and didn't go a single foot, DRT. Bullet broke front leg and liquefied the heart. Bullet was just under off side skin.