If you want a handgun for your primary tool for hunting feral hogs, you need something you can consistently fire accurately at 50 yards or more, with as much power as you can handle. Personally, I don't think most folks will ever practice enough with a high powered hunting handgun to be consistently accurate at longer distances than about 15 yards. Were I interested in handgun hunting, .44 magnum with a heavy load would be my choice, because it is very accurate at medium ranges and packs a decent punch, without being overwhelming in the recoil department. The more powerful chamberings available are even better, but require a good bit of expensive practice to de-sensitize oneself to the extra recoil.
Certainly, a .357 magnum has enough power to kill most animals, if fired into the 'vitals,' but don't expect a one-shot stop unless you can place the bullet into the brain or the heart. I killed a medium sized feral hog during last dove season, with my carry gun, a .45 ACP, because another hunter had gut-shot it with a rifle, and I wanted to finish it off, rather than leave it to bleed out over a period of several hours. It was getting too dark for a rifle scope at close range, in moderately brushy country, so I took the pistol and intended to chase it down and finish it at close range. As it turned out, the hog was still very much alive, and managed to keep 30-40 yards ahead of me, ducking around in the brush and hiding till I came close, then taking off again. I managed to get three rounds into his lower chest cavity, that had no measurable effect on his ability to escape. I finally managed to bounce a round off his skull, at about 35 yards, just as he was about to disappear into some thicker brush, where I would not have followed him. It knocked him silly for just long enough to allow me to gallop up to him and shoot him behind the ear at close range. It was an altogether unpleasant experience for me, because I consider myself a humane hunter and will normally not take a shot on a game animal until I am confident that I can make a one-shot kill.
Personally, I use a 7mm-08 or .30-06 rifle for that size game. I would use a 12 or 20 gauge slug if I was confident of my accuracy with it at ranges over 50 yards, and I have a 10mm pistol that I might be confident to use at under 25 yards, with the right shot opportunity, and if I had been having good practice sessions with it. A .357 magnum that I shoot well would fit into that 'under 25 yard' category, and I would probably be aiming at the head, unless I was sure about the heart location at that particular angle.
This is all just personal experience (and opinion), and I admit that I am not a great handgun marksman, so take my story for whatever it's worth to you.