I know that this thread is more than a year old, but in case anyone else finds their way here, I wanted to offer a more complete answer. I should say I wanted to link to someone else who has a more complete answer:
https://www.youtube.com/watch?v=iLiEPzHDbzA
I have done quite a bit of research as I have been building an AR-10 and trying to finalize what round to use. Essentially the two are so similar, take your pick. However, there are a couple of situations where one has a more clear advantage over the other:
1. If hand loading for max BC bullets for long-range shooting in an AR-10 platform, the 6.5 CM has an advantage due to the fact that heavier 7mm bullets have to be seated deeper to fit the AR-10 magazine. You will not realize the full potential of the 7mm-08 in this rifle. No compromises with the 6.5, which already has a slight wind advantage at long ranges.
2. If loading for hunting with a bolt action that has a faster rate of twist, the 7mm-08 has better terminal energy, albeit not by a tremendous amount.
Fans of each cartridge will point out the advantages of their preferred round, but again, the differences are relatively small. If you already own one, no reason to go buy a new rifle in the other - except of course, to have a new rifle in a new caliber.