Personally I think you will get better performance on GAME with a 6.8 SPC barrel and my second choice would be 5.56 with plain old 55 gr SP, keeping range in mind. This has been my experience as well as the experience of many others.
The larger 6.8 diameter increases terminal performance, this being the correct observation of the original military evaluation during SPC development when tested vs. 6.5 diameter bullets on actual flesh and bone. Source: American Rifleman,
Remington's 6.8X43 History And Development, Dec. 2021 :
https://www.americanrifleman.org/content/remington-s-6-8x43-mm-spc-history-performance/
"Many 6 mm, 6.5 mm, 6.8 mm, 7 mm, and 7.62 mm cartridges were considered and tested, but it was ultimately decided that the 6.8x43 mm Special Purpose Cartridge (SPC), with a 115-gr. bullet moving at 2600 f.p.s. from the muzzle offered the best combination of accuracy, lethality and reliability."
6.8 SPC is also likely to have a slight energy advantage at ranges where almost all game is shot with these rifles, due to higher muzzle velocities acheived bullet weight-for bullet weight. Hodgdon shows 2608 for Grrendel vs. 2711 for the 6.8 SPC for 110 gr. loads for example.
6.5 is a better target round, being higher in BC though slightly slower. Its larger head means less metal on the bolt and weaker bolts.
Published in Shotgun News, July 31, 2006:
"Its head and body diameters are larger than 5.56 (0.378 inch), but smaller than 7.62x39mm (0.445 inch). This thoroughly obsolete cartridge was chosen as the parent case because its smaller head diameter (0.422 inch) required less metal to be cut from the bolt head compared to the PPC or 7.62x39mm cases, which improves bolt service life."
6.8 SPC feeds and functions very slick through an AR. I dont know if anyone has ever done a military style evaluation of mean rounds between stoppages, but if they did 6.8 SPC would win every time.
SO for hunting, and reliability 6.8 SPC is slightly ahead, for paper punching 6.5 G gets the nod here.