I have 300blk, 6.8, and 308. I thought hard about 6.5 Grendel, 6.8, and 277 and went 6.8 due to factory ammo availability.
300 black is best if you want a 8" or 10" barrel. Should kill deer to 200 yards with supers. I have not fallen in love with 300 black. its main function is suppressor use or PDW in my opinion.
277 is better than 300 black, but not as good in short barrels. 277 ammo is hard to come by. You would have to reload and give up power and range to Grendel and 6.8. It should be fine to 200 yards on deer. Maybe even 300yd.
6.5G and 6.8 are splitting hairs to me. Both need special bolts and magazines, but that's no big deal. Both should be good on deer to 400 yards WITH THE RIGHT AMMO. I consider 6.8 better for hunting and Grendel better for long range paper.
6.8 has more factory ammo for hunting. It throws bullets as heavy as 120gr over 2500fps from a 16". Mine likes factory 95gr TTSX's at 2,775 from a 16" and groups 5 shots from 5/8" to 2" @ 100yd depending on how clean the barrel is. Hornady HPBT match is 1 MOA.
6.5 Grendel is getting more options for ammo, but less selection than 6.8. Despite less selections, the few factory offerings are all you would need anyway. Wolf makes cheap plinking ammo even. Over 400 yds, Grendel walks off and leaves the 6.8.