I think the caliber consideration is secondary to the energy at a distance. A high power .177 will kill a deer with the right shot placement at the right distance all you need to do it punch through the skull at just the right place. But that is not usually a realistic shot. I believe it's best to treat shot choice on large game as you would for bow hunting and limit head shots to an absolutely sure thing. Therefore, the likelihood is that it wont be a DRT (Dead Right There) shot, but rather you will need to follow a blood trail to find them in most cases. The best shot for that is not only one to a vital area, but one with a complete pass through, giving both an entrance and exit wound to bleed from. And for that, the ballistic energy holds a little more sway than caliber choice.
The minimum I would consider for hogs or deer would be 300 ft lbs, but I would be more comfortable taking the shot if I knew there was more than that on tap unless I was very close. My state (GA) went with a minimum of .30, but I could not find any that had what I was comfortable with in the power range I wanted. Due to my specific hunting conditions - spot stalking in thick swamp cover - portability and maneuverability were also prime considerations, so I went with the Texan .457 Carbine CF. If your conditions permit, a longer barrel would be better due to the energy it helps produce. The minimum I would consider would be .357. My favorite is a mute point since I have not personally used anything for large game other than the .457. But with that, I can tell you it will flip a coyote over backwards with a center chest shot at 35 yards.