When you say "no extreme distances" can you narrow that down to say, a max distance? Many of the AR cartridges begin to show the major differences at around 200 yards. Things like 6.5 Grendal, 30 AR, 6 ARC are your power houses in terms of energy, and out to long distances (300+). Pretty much everything else is beginning to die between 150 and 300 yards. Deer and hogs are two pretty disparate animals when it comes to punching them. Deer drop pretty readily with almost anything, hogs are nature's little tanks.
Personally, I'm not a fan of 7.62x39 for a hunting round. Because of it's odd bullet size, there aren't nearly the bullet choices that you'll find for mainstream calibers. It's kind of the rifle version of the 9mm Makarov. It's there, it's on par ballistically to several other rounds, but just doesn't set itself apart enough.
I get a 30 cal is a bigger diameter than a 6.5, but we're talking, literally a millimeter. The Grendel more than makes up the difference in velocity (i.e. energy). If you're down on velocity or energy, then you need to go a lot bigger in diameter to make up for it. When you go big, then you lose BC and range, so it's always a trade off. For example, 450 Bushmaster, 350 Legend, punches a big fat hole, but the stubby bricks for bullets don't hold their energy for much past about 150 to 200 yards.