The 6.8 has far more ammo, uppers, barrels, and product availability. If you need to buy ammo, it's out on the internet. 6.5G ammo had become a such a sticking point that Les Baer ordered his own cases to remedy the problem.
In terms of ballistics, both will do. At 200-300 yards, the typical 6.8 load will be in it's optimum range. The 6.5G offers a more efficient bullet that delivers better performance further. Whether anyone actually shoots game past 400m is the real issue. Most never do, unless it's prairie dog or antelope. If that is also on the table, get the 6.5G and always keep a box ahead of your shooting.
The majority of the AR shooters using something besides 5.56 use 6.8 SPC. Argue ballistics all day, the sales figures are there, and so are the suppliers. Most hunters prefer more power at shorter ranges.
For the AR enthusiast, the 6.8 offers less modification to work right. The AR was designed for a slight taper small case, and the 6.8 does push that. It requires a barrel, bolt, and magazines. All of those are open market items. The 6.5G also needs a barrel, bolt, and magazine, and therein lies the rub. The case diameter becomes so large the makers offer superbolts, even they think standard AR bolts are weakened too much. The magazine makers have the biggest challenge, making a curved magazine jog into a straight mag well. Keep the mag under 20 rounds, and it is much less a problem, and possibly a hunting requirement. The point is using tapered Russian cases in the AR means accepting compromises. The benefits have compensating problems.
The 6.8 SPC was designed in the AR action to make it all work within it's limits, the 6.5G was designed to get the best possible performance at long range, with some compromises that were acceptable for precision shooting. They aren't major sticking points, but need to be out where you can see them and fully assess. Which you choose isn't a test of moral fiber, just get what looks like will work best for your conditions.