Sure your not thinking of a 375 Winchester? I have a 375 Marlin that makes and excellent hog gun for the reasons you state.
But the 375 H&H is a belted magnum cartridge. The 375 H&H may use a big bullet, but it has a large case and tremendous punch over 4000 ft lbs energy at the muzzle. Some like the Hornady load are much higher like the 270 GR Bullet reporting a Muzzle Energy of 4937 ft lbs and Muzzle Velocity of 2870 fps.
I'm surprised that C.B. isn't speaking up here. He uses the .375 H&H for most everything above a rabbit and makes a fairly persuasive argument for doing so.
460 S&W is a hog hammer. 450 marlin ruins their day. 480 ruger stops them dead. I haven't put a 500 on one yet, but i sure do want to. Oh, and anything that says "Weatherby Magnum" works really well too.
500 works great if you wanna go deaf. I would suggest you take your pistol of choice as a backup or primary if in close. Which ever long gun you choose, put the crosshairs on the ear and your makin bacon. If you take out mama first you can usually get a bunch of her little squeallers too.
Good Hunting!
Mr E - AMEN with that comment. Use enough gun for the job and take Momma out first. You know a .22 short behind the ear makes her DRT but gettin the proper angle is something else.
Coool! I like.
That gun would be so much fun for shooting hogs out in the wheat field on one place I hunt. I could shoot them from the front porch of the hunting cabin.