This discussion brings to mind an article I read not long ago where a scientist actually did some hard research on energy vs. momentum to determine what kind of WOUND would be produced by various projectiles. His results are very, very interesting. You can check this out at the following website:
http://www.kineticpulse.us/math/kp.html"Stopping power" is a function of wounding, that is how big the wound is and how much trauma force is absorbed by the wounded animal. Based on his (IMO reasonable) research, the 7/8 once 20 ga slug traveling at 1509 fps mentioned below will create about TWICE the trauma wound in a hog as a 100 grain .243 bullet traveling at 3100 fps, PROVIDED BOTH STOP IN THE ANIMAL. If a bullet or slug goes through the animal, then the wound is reduced by a factor proportional to the velocity/energy of the exiting bullet. If you want STOPPING POWER from the .243 then you need a frangible bullet that will not exit or will do so with as little velocity/energy as possible. That might explain why the 100 gr partitions mentioned above were not good stoppers. It also explains the statements above that deer "knocked off their feet" when hit by slugs.
I would not hesitate to use the 20 ga slug on hogs, especially if you want the hog to drop in its tracks. Definitely I would choose it over the .243 for pure stopping power with a close-range offhand shot. However, if at all possible, I would prefer to work on hogs at a distance of more than 50 yards from a solid rest, where the .243 would be ideal for the accurate head/spine shot that would floor it. Pressed to do my work inside 50 yards, then I would want to be carrying the shotgun with slugs.
Probably the ideal setup with a .243 would be either to get off the ground with the .243 and take head/spine shots with expanding bullets (jacketed soft points), or to take a careful first shot at a distance from the ground with the same .243 loads, keeping a big-bore shotgun or sidearm handy for close-in work. I would stay away from heart/lung area shots with high-velocity, small-diameter bullets, especially those constructed for no expansion or limited expansion (core-lokts, interlocks, partitions, A-frames, X's, core-bonded, etc.). Heavier bullets of 140 grain or more at modest velocities with rapid-expansion bullets will and do work fine on shoulder shots; in fact they are spectacular "drop in their tracks" hog-stoppers in my own experience (2 hogs with 140 gr .264 soft point bullets at 24-2500 fps = 2 x zero travel post-hit).