Honestly, what's the use? Both have their ups and downs.
6.8 is not as barrel dependent as the 6.5. It was designed for 16 inch barrels and has a fast burning powder so it's already got it's giddy up by the time it's left the muzzle. 6.5G on the other hand only really starts to shine after 16 inches of barrel and really comes into it's known range and accuracy in about 18-20 inches.
However...
The 6.5G will beat the 6.8 six ways to Sunday in the accuracy department, especially when talking 18 inch barrel. There is no doubt worldwide, the 6.5 caliber is king of the long range shooting. Whether it's a 6.5 Creedmore, 6.5 Lapua, .260 Remington, 6.5 Swede, etc, most long range shooters will tell you the 6.5 gets it done just as easily as any .30 caliber.
But for us common man, the ranges of 500 yards or less, it's flip a coin. Both are accurate enough within that range. However, start going beyond 500 and the 6.5, especially out of a longer barrel (say 18 inches) really starts to become a great rifle caliber. There is slightly more availability with 6.8 factory loadings right now, but that's changing. Both have proprietary magazines, bolts and barrels. Both have greater ballistics than the 5.56 out to range.
Flip a coin. Either one will serve you well.
Basically, if I had to pick a single fighting rifle and could have unlimited ammo for a SHTF scenario, I'd probably go with a 6.5 Grendel in an 18 inch barrel with a 1-8 adjustable scope and the Hornady 123 grain SST. While I wouldn't feel under-gunned with a 5.56 or a 6.8, the ability to reach out further and say hello to my little friend gives a distinct advantage to the 6.5 Grendel.