The 6.5 bullets usually have a slightly better BC than 7mm in your standard 130-150gr hunting offerings. However, the 7mm-08 does have a little bit more schlitz, due to the case capacity that the Creedmoor gives up to fit long high BC bullets into a standard short action or AR-10 mag.
Those are all theoretically differences though. You'll find as much or more variation between individual loadings from various manufacturers as you will between the two cartridges themselves. In reality, if 1" of drop or 100fps of velocity is making the difference between a successful or unsuccessful shot, you're way too close to the margins to be taking it.
In today's market, buy what ammo you can find, and get the rifle to match. 7mm-08 should be easier to find, as it's not quite as much in demand as 6.5CM.
If you really want more performance, look at cartridges based on the '06 case. 6.5-06, 270, or 280 will all outperform their smaller cousins, and by an actual noticeable margin.