The thread is about hunting and 200m shots at live game.
For that, the 6.8 or 6.5 would be better as they are offered in hunting ammo, have about 5 years more development toward that goal, and the market offers more hunting choices.
In use, the gun could be sighted in for a longer point blank range which would reduce the holdover guesstimation a younger shooter would need for the slower .30 bullets.
This really isn't a discussion of how one or the other would handload it - it's about choosing the better live target application. 6.8 or 6.5 is a better choice, and between the two, 6.8 offers a lot more ammo diversity. Go 6.8.
The .300 AAC was pretty much designed for just such emergencies. Advertised to allow people who aren't legally allowed to use .223 to use an AR style rifle.
This is a false claim by AAC. The .300BO was originally developed by SSK as a suppressed round, not supersonic. It was predated by early 3Gun wildcatters trying to get the AR15 into competition. The rules then expressly prohibited anything but .30 and up as Real Men didn't use poodleshooters. Regardless that some competitors came up with a rules legal .30 x 5.56 round, they were tossed off the courses. Eventually the AR15 was accepted - but nobody bothered to make .300 WHISPER a competitive round, because, it isn't. Higher loaded ammo costs and more bullet drop aren't attractive qualities.
As for "who" came up with a hunting round to use where .223 wasn't allowed, NONE were "developed" for that purpose. The early .300's were a dodge around competition rules, 6.8 was a Special Forces/AMU project to increase power 50% over 5.56, and the 6.5 was intended and did earn long distance precision target competition awards. Only the 6.8 was intended for use on live targets at range - which should be enough reason to choose it. And many many do.
What we have is a market place that pushes the lastest Cartridge of the Month, vs calculating what cartridge you need for that specific task. If it's a live target, go with ballistics, not some arcane discussion of handloading. It's about reach and power, not what bullet neck it might have. 6.8 has the reach and power above and beyond 5.56, which is where it counts. .300BO might show some nice numbers if you pick and choose them, but the amount of long range hunting ammo on the market shelf is much more limited because a lot of .300BO shooters aren't creating much demand. 6.8 did and has.
Here's the "metric" to consider - how far will the round hold 1,000 foot pounds of force? That's the commonly accepted ethical minimum, and at that range, it's also an example of how efficient the bullet shape will be holding it. Look at the numbers and also the hold over to keep it on target, then choose. At least it will be based on it's actual reach and power, not an internet discussion between two players attempting to pull rank in their imagined social hierarchy. The goal is a downed animal taken cleanly.