I own and shoot both the 6.8 and 6.5. I have yet to take any large game with the 6.8 as I built it right before deer season and had no luck. However, I was able to get a cow elk with the 6.5 and a 100 grain Barnes TTSX loaded with 28 grains of AA2230. Those rounds had a chrono reading of about 2795-2800 fps. I could have probably put another grain or two of powder into them for another 100fps out of my 20 inch barrel. My shot was HORRIBLE. I hit the right rear femur as the elk was running at an angle away from me. The bullet broke the femur and passed another 2-1/2 to 3 feeth through the body and finally stopped just under the hide on the left front shoulder. Luckily the bullet caught something vital and she died after she layed down on the opposite side of the hill that I shot her on. The bullet penetrated a lot better than expected after hitting the femur. You can see where I cut the bullet out of her shoulder in this picture.
I think the bullet would have opened up a little more had it not hit the femur right off the bat.
Now, I believe that either round is capable of taking most game at reasonable distances. The 6.8 is a fine round and it is great for killing anything that you want it to. As Bedlamite points out, the 6.8 basically focuses mostly on various hunting rounds to load for it because the match bullets really don't have the best of BCs. The SPCII chamber was not designed for match accuracy either so you should not expect to get totally amazing groups (though some guys do). I personally think that the 6.8 is a perfectly good round for hunting. I think that the best bullet for the 6.8 right now is the 95 grain TTSX.
However, I personally prefer the 6.5 Grendel. It is true that most of the high BC bullets that the 6.5 Grendel can use are not designed for hunting. That said, the 6.5 range of bullets gives one plenty of hunting bullet options, though they don't have the high BC of the match bullets. The 6.5 bullets do seem to work pretty well on game. I personally don't think I will use anything but the Barnes TTSX 100 grain bullet because I think you get the most bang for you buck from that bullet. There are a lot of guys using the new 123 grain AMAX which will probably work as well as most hunting rounds. There are already a few guys reporting good results on deer.
The reason I like the Grendel is because my rifle can double as a long-distance, high-accuracy range toy AND it will kill a deer or elk as well as the 6.8. There are some that contend (stupidly) that the 6.8 is as good of a long range caliber as the Grendel, but in all actuallity BC really does mean something -especially when wind is added as a factor. So, when I want to shoot it for accuracy I can load some match bullets with high BC; when I want to shoot animals I can load it with some good hunting bullets.
Both the 6.8 and the 6.5 are going to cost about the same as any other good hunting load if you are buying factory ammo. Now that Hornady is producing brass for 6.5 grendel, both 6.8 and 6.5 reloading components are readily available and similar in price. I have found that the 100 grain TTSX 6.5 bullets are easier to come by than the 95 grain 6.8 TTSX, but that could just be in my area.
Also, the 6.5 grendel is short on makers of magazines but I have found that the 6.8 mags acutally work really well in my 6.5 Grendel and vise-versa. So, if you want to buy a high dollar 6.8 mag and use it in the 6.5 grendel, it should work well.
I won't tell you what to buy, but I will say that if I was to start all over again and I could only get one, I would definately go with the 6.5 Grendel. It's just more fun for me and does everything I want it to do.
Just for more information here is an article that I found kind of interesting.
http://www.ar15.com/forums/topic.html?b=2&f=431&t=202148&light=