The presumption that the military is somehow restricted to FMJ is in error. They are not.
What is presumed to be an agreement in the Hague Conventions is a restriction to using bullets designed to expand, with either a cut away exposed lead core, or hollow point. It reflected the nature of "just war" ethics in the day, including the primitive medical care available.
What may have resulted in the expedient use of FMJ was more based on what the researchers and designers saw as the real intent of combat - to reduce the ability to fight back by an organized unit. And that doesn't mean you have to shoot them Dead Right There. It's a civilian presumption. What you have to do is get the other soldier to quit shooting back. That is usually accomplished by hitting him with a bullet from your side of the conflict.
Another error made is assuming that it's actively aimed fire. It doesn't have to be - in fact, a significant number of wounded and dead in an active firefight are hit by a round that was never deliberately targeting them. They either moved into the line of fire, or were hit by a ricochet. Random friendly fire is also known to have some affect.
One component of that fire is that it well may have been aimed fire at the barrier a soldier was hiding behind. That is a common tactic, and one ammo designers must address in combat ammo. It does no good to use a quickly expanding round with minimal penetration if all it does is splatter on contact with stone, adobe, building material, dirt, gravel, sheet metal, wooden construction, etc.
Since military ammo is required to penetrate to hit a target soldier in those conditions, then the bullet is designed and constructed to do that. And in the production process, it can be expediently and more cheaply done by stretching a gilding jacket with closed nose, then, loading it with the lead and other ingredients - like, a steel penetrator. And if you can get it to break in half on contact at the cannelure so that it becomes multiple projectiles, so much the better.
That is exactly what our current technology in battlefield ammo is delivering to our soldiers.
For long distance use, another trend was researched, and it was discovered that bullets like the Sierra Matchking. It was developed in the early '50s, and to get the characteristics of having a bullet with a boat tail, weighted toward the rear, with a light nose, it was easier to produce it with an open tip. Note - open tip, not "hollow point." The distinctive difference is that it is not designed for maximum expansion with petals or cutaway open nose, it's designed for long distance ballistic performance, which it proved in Olympic shooting, and where that design still dominates.
Being the choice of long distance shooters, and that the Army uses same as snipers, it was researched extensively. The JAG came out with an opinion in the 1980's that open tip match bullets conformed to the Hague convention and were legal in international conflict. At first glance,they look like FMJ, too.
There is no requirement to use FMJ, it's just how we make our bullets.
How does that resolve whether the 6.8 or 6.5 is "better?" Not at all, there never will be a resolution. It's wrong to try. They were never designed to do the same thing, they never competed in the same events, and it's only the civilian fanboy who does on the internet, because he hitches his ego to a star and thus his self image as a shooter.
And if I remember correctly, some variant of the 6mm PPC holds the record that the 6.5 previously won in long distance competitive shooting using AR15's. Moot point why I would want to use it deer hunting out of a 16" barrel, as the round diminishes in ability more severely in shorter barrels. That is because it uses a slower powder that requires more barrel length to reach it's optimum speed for it's design intent, shooting the more efficiently shaped bullet to longer distances. If you antelope hunt, shoot ground hogs, or have wide ranging vistas for mule or whitetail deer, 6.5 would offer an edge. The tradeoff would be the 20-24" barrel. You could do as well with an 18" .308.
In most of the American heartland where whitetail live in broken woodland and edges, the shorter 6.8 16" AR would perform better, for the same reasons that the Winchester 94 did compared to a Mauser/Springfield bolt action in it's day. Short, light, less recoil, and a faster follow up shot. Entirely where we are today in combat arms.
No winners or losers except the guys who do or don't know how to match the cartridge to what they are shooting at. You don't use a framing hammer on a jewelry box, you don't use a small ball peen to set spikes in landscape timbers. Unless, of course, you think of things only by Brand name and how it reflects on your self image. Neither one rules the roost, they are simply better than the other at what they are designed to do.
If you are looking for another cartridge in the AR15, there are choices, make an informed one and you'll be more satisfied.