To me the appeal of the Blackout is as a round for use in suppressed weapons. For that purpose one is limited to subsonic velocities so the only gains in performance are made with greater bullet diameter and weight. A 220gr subsonic .30 caliber would fit the purpose within a couple of hundred meters.

Also, within a couple of hundred meters, the 5.56, especially with some of the heavier loads, is quite a formidable weapon and does a decent job penetrating obstacles and body armor. No, it isn't a 7.62 or a 338 Lapua, but neither does it weigh as much. All in all the M16/M4 is an exceptional weapon with the cartridge it was designed to shoot. If one doesn't need to shoot with a suppressor and the range is within 200 meters, the Blackout offers little, if anything, over the 5.56 shooting heavy bullets.

So, to the topic at hand, given only the choice of 300 Blackout vs 5.56 in an AR:

If I needed to shoot a suppressed AR I would choose the Blackout.
If I wanted to use the rifle for deer/pig type hunting within 200 meters I would choose the Blackout.
If I wanted to use the rifle for hunting varmints or for any other use I would choose the 5.56.

Limitations of both the Blackout and the 5.56 begin to become apparent when engaging targets much beyond 200 meters. And it is at these greater distances that the benefits of cartridges like the 6.5 Grendel and the 6.8 SPC are realized.

Regarding the .300 Blackout vs the 7.62x39. Here is what AAC has to say. Note that one of their goals was to match 7.62x39 ballistics. Also, they explain why the 7.62x39 didn't meet their purpose.

DESIGN OBJECTIVES
• Create a reliable compact 30-cal solution for the AR platform
• Utilize existing inventory magazines while retaining their full capacity
• Create the optimal platform for sound and flash suppressed fire
• Create compatible supersonic ammo that matches 7.62x39 ballistics
• Provide the ability to penetrate barriers with high-mass projectiles
• Provide all capabilities in a lightweight, durable, low recoiling package

REASONS 7.62x39 wAS NOT CONSIDERED
Extreme cartridge taper
• Reduces reliability of feeding in AR Magazines
• Reduces Magazine capacity
• Cartridge taper induces considerably higher bolt thrust-
exacerbating the AR Bolt's weaknesses
• Requires a larger Bolt Face which reduces Bolt Locking Lug strength-
exacerbating the AR Bolt's weaknesses
Limited projectile selection
• 0.311" diameter not a common option in most modern bullets