I'll admit up front that I'm a big 308/7,62x51 fan. Considering the size a pig can attain, this would be my first choice. The downside are recoil (recovery time) and ammo cost. Keep in mind that a SLR will most likely throw those expensive cases into the thickets. Berdan-primed (steel cased?) milsurp ammo solves that issue, but usually comes with FMJ bullets that are not as effective. Some recoil-control measures might be usefull. A supressor with external brake might help, but add weight and bulk.

Next down the line is the 7,62x39. Inexpensive, non reloadable ammo is available, but also loaded with FMJ's. The S&B JSP ammo is an option, but the nice reloadable cases will still get lost. Maybe get something that can accomodate a case-catcher? The AK-platform has some difficulty in getting it scoped, as the scope mounts are not all very sturdy and cheek weld becomes an issue. Pig hunting usually requires a rifle-sight combo that can take a few knocks.

In 223/5,56x45 you have many options in guns, but very little effectiveness in the ammo. I would only consider premium expanding bullets like a Barnes X or a similar monolithic (or bonded) version. Even then, it is a marginal calibre on a big boar. Shot placement will be critical, meaning you loose much of the advantage of a fast shooting ability. You might still want to catch the cases.