For some, 6.8 makes the AR15 a legal shooter in their state under their game laws. No contest there.
For live game hunters - where the big emphasis has been - 6.8 offers more power downrange at typical distances than 5.56. Simple ballistic fact. You'll find many who claim the 5.56 will do a good job on deer, either requires proper shot placement, and even I have seen deer shot with .308 who run a hundred yards. No cartridge is guaranteed a one shot stop. You want that, get a 8mm Remington Magnum, and you have a much higher percentage of doing it.
Bullet TYPE has a lot to do with it - cheap 7.62x39 is often Not Legal To Hunt, being cheap full metal jacket. Load it with decent expansion hunting bullets, and guess what, it's $20 a box. Any cartridge is, commercial ammo never sells for what cheap surplus does. Don't confuse the real issue.
You want cheap plinking ammo for gravel pits, don't buy a commercial caliber, duh. You want to shoot LIVE game in the field in the AR15, the 6.8 will get results without having to carry a gun two pounds heavier with 20 more pounds of recoil. As someone who DID carry those guns in the day, I find it significant. The AR doesn't wear me out the way a HK91 or 30-.06 bolt gun does. A 16" carbine in 6.8 is just a lot easier to use if you're already experienced with it.
There's the issue - 6.8 is fine, but being familiar with using the weapon in the typical "drive by" shooting that deer offer in the woods is more important. Focus on the overall use with the choice of caliber as one aspect of it, not the caliber as the focus and ignore how you and the gun interact to get the job done. Some are just more comfortable with bolts and levers, fine. They can decide to enhance their use with 6.8, too, where it fits in.
6.8 is a great improvement over 5.56 in knocking down 150 pound mammals, exactly what it was designed to do by Special Forces and the Army Marksmanship Unit. It's not the heaviest hitting, or the longest ranging, or uses the highest BC bullets, or the cheapest. But line up all the factors for the leading contenders, pro and con, and it's a top tier choice overall for the job - shooting live game in field conditions.
Where the detractors get any traction is nitpicking it outside that performance envelope, where they can "prove" their choice is better. At that point it all oranges against the apple, note carefully they target 6.8 as the contender, which means they see it as a tough competitor to knock down. Otherwise, the talk would be all about how their choice is better than 5.56.