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Stick to the .308
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I'll second this, provided you want to see them on the ground dead without much tracking.
If you're just reducing the hog population, with no concern for recovery, then 5.56 will kill them deader than a hammer, they just run further.
Most hog hunters will tell you that if you catch them right in the spine between shoulders and ears, they drop right there with any caliber.
My only experience killing hogs is limited to 3.
Two of these where by a 45-70 shooting max loads behind a 350 gr Hornady JSP at roughly 25 yards. I never felt as though I had used too much gun. One of them dropped in his tracks after being shot in the neck but managed to flop around for several minutes. The second one got nailed right in the shoulder and still managed to run a good 50 yards into dense cover making the tracking job unpleasant. Pictures and details of this are located in this thread:
https://www.ar15.com/forums/t_10_9/682217_Where_are_the_45_70_s____.html
The third I took with a 357 mag using a max load behind a 158 gr. Hornady XTP at roughly 15 yards. Despite taking out both lungs and having a exit wound the size of a quarter, everyone in my group originally thought I had missed it because it acted as if a hair had not been touched and had zero blood trail. By sheer luck, it expired in the middle of the four wheeler trail we were riding back to camp on, about 200 yards from where it'd been shot.
Hogs are definitely not bullet proof, but I don't think anyone can say they're not a whole lot tougher than a deer. For this reason, I'll always take the bigger gun if given a choice hog hunting.