I just got done buying everything I need in order to build a 6.5 grendel which I will also use for hunting deer. Then I realized after looking at charts that the 6ARC holds more energy out to distance. I know it's not what you asked but just pointing it out because I now wish I would have gone that route.
The heaviest hunting bullets for 6mm are generally topping out at ~100gr with pretty low BCs, with the new 103gr ELD-X being the main exception if you can find them.
From a 16” barrel, velocities will be roughly the same with same bullet weights, though 6.5mm can probably generate 50fps faster on average since it isn’t as constrained in the neck (overbore) and has a little more case capacity.
With 6.5 Grendel, you can shoot everything from 85gr on up to 160gr, but 129gr and 130gr are common for the heavier loads, with multiple factory options in those weights. There are a lot of 85-130gr hunting bullets for 6.5 Grendel.
From 16” barrels, I’m not seeing any performance advantages for 6mm ARC even with the 103gr ELD-X, which is the highest BC/heaviest hunting bullet I’m aware of that you can shoot in it.
Here are the reference rifles I’m using for extrapolating velocity data from:
18” Noveske 6mm ARC, Hornady published Gas Gun load data with 103gr ELD-X at 2550fps with the 2 fastest powders when hand-loaded.
24” 6mm ARC 103gr ELD-X 2750fps per Hornady
6mm ARC 16”, 103gr ELD-X (.512 G1 BC Hornady), 2500fps (I rounded up from 2492fps.)
200yds 2174fps 1081ft-lbs
300yds 2021fps 934ft-lbs
6.5 Grendel 16”, 123gr SST, Litz .462 G1 BC (lower than Hornady’s .512), 2440fps
200yds 2085fps 1188ft-lbs
300yds 1920fps 1007ft-lbs
The main place you will see an advantage with the higher BC 6mm target bullets is from long barrels, with trajectory more like a 6.5CM. I think that’s where 6mm AR really shines, with light recoil/ease of sight picture management. This is my experience with 6mm AR, shooting either 20” or 26” heavy barreled AR-15s set-up for competition, not anything shorter or lighter that would be appropriate for hunting.
You can add more barrel length to 6.5 Grendel and shoot 135gr A-TIP to compete with 6mm and retain more energy on-target, but the barrel length with be something to consider.
When shooting 120gr, 123gr, and 129gr from 6.5 Grendel, you will certainly see a bit more sight picture disturbance than a 103gr in the 6mm, but it’s still manageable.
When doing load development or shooting groups, it’s easier to group with the lighter weight bullets for me, regardless of cartridge. Shooting 107gr SMKs through either feels the same, as long as the rifle weight is the same.
The 6mm has more lightweight bullet options for varmint work, and the 105-108gr class of TGT bullets have higher BCs than the 123gr class in 6.5mm, while going faster than what you can make a 123gr do in Grendel, barrels lengths equal.
Conclusions
For a practical hunter in lightweight AR-15s, I think the 6.5 Grendel makes more sense because you just have so many more bullets to choose from for heavier game, while still being able to shoot varmint weights.