I have both 6.8 and 6.5 Grendel. I doubt anyone could tell the difference on game. Bullet selection for 6.5G is far superior, and the 6.5 will reach much farther. 6.8 is far more available, and can be found in most gun shops on the shelf. The lack of 6.5 ammo and brass is quite frustrating, and while Lapua 6.5G brass is nice, almost a dollar per piece is not what I'd call cheap.
Unless you handload, I would not recommend 6.5 Grendel. I'd class it as a popular wildcat, rather than a true commercial round whereas 6.8 is more like a not so popular factory load.
As far as accuracy, both cartridges can turn out some outstanding groups. Here the 6.5 clearly has the advantage of a huge selection of match grade bullets. The 6.8, limited to lighter 0.277 bullets, has a pretty limited selection.
I'm also uncertain what the previous poster means when he says 'BC', but in the BC (ballistic coefficient) department 0.277 bullets don;t even come close to what is available for the 6.5, and the light bullets required by the 6.8 have the lowest BC of al the 0.277 bullets (not that any are particularly great).