300 blk shines as a suppressed subsonic slinger in a short-barreled configuration. But that isn't the only reason to consider it. 300 blk shares everything but the barrel with your 5.56 if you already have one. Has around a 30% increase in energy over 5.56 at all barrel lengths. Has options, though pricey, that will expand down to very low velocities. Is very effective for killing at the most typical hunting ranges (50-150 yards).
I skipped over the 6.8 and went straight to the 6.5 Grendel for my longer range work. I would not hesitate to shoot a deer at 500 yards with my Grendel if presented the opportunity.