All around is pretty vague.
One thing to consider is that the 6.8 won't need a 20" barrel - it was designed and intended for a 14.5", at 16" it's already gained. With some of the smaller loads, shooters are chronographing speeds nearly identical to 5.56. What that delivers is the extra foot pounds of force from the increase in mass, making it deliver even more power to handle larger game more efficiently.
That makes the choice more like a 20" 5.56, or a 16" 6.8, which then adds the difference of rifle vs carbine. Now we're talking overall size, where and how you hunt, etc. I've used the M16 for decades in the service, and built a 6.8 with 16" barrel for myself. I preferred the advantages of lighter weight, shorter barrel, and more power on deer. That's what the rifle does most of the time.
All around is a nice goal, but what the rifle will do 85% of the time is the reality. Choose the caliber and barrel length to fit that job, and the rest will be easier.