I haven't done either, but my guess is that a 375 H&H would probably make less of a mess than a 25-06 if you happened to clip the shoulder of a deer inside 200 yds or so.
THIS ^^^^ is exactly correct.
A 375 is just like any other dangerous game rifle. But if you're shooting solids they do less damage than a 22-250 or 243. Just an entrance and exit hole on small game.
This is also correct except you can add in expanding bullets as they do less meat damage as well.
Would .375 H&H for hog hunting be overkilled?
I am going to throw in my $.02 for what it's worth as I have killed a bunch of light game with heavy DG rounds. Including the .375H&H, .404 Jeffery, .416 Remington, .458 Lott, .470NE, and I've seen light animals killed with the .500 NE and .500 Jeffery.
First off the .375H&H gets WAY more credit for being a "heavy" caliber than it deserves and that's because it kills game and acts like it should be a heavy caliber. But in reality it's not. The .375H&H is at the very bottom end of the legal
medium calibers for dangerous game hunting. It puts out just over 4,000 Ftlbs of energy with a 270 or a 300 gr bullet. The rifle is very flat shooting with a 250 or a 270 gr bullet and with a 300 or 350 gr bullet tends to act just like one of it bigger 40 cal+ cousins on game. With the 270 or 250 gr loads act more like a .338 or big .30-06.
Almost all of the new super zipper .33's like the RUM's and Weatherby and such put out more muzzle energy than a .375H&H heck a .300 Weatherby class .308 with a 180 bullet matches the energy of a .375 H&H. I don't consider a round to be a "heavy" until we get to .458 cal and up, 500gr bullet and up and then it has to put out 5,000 lbs + muzzle energy. I think that there is a lot of overestimation and misunderstanding about the .375H&H due to it's African roots and the stories that people read about it that tend to place it in the realm of African heavy game hunting legend. Capstick wrote about the .375 as if it were the hammer of Thor. It's really not all that powerful but it does kill far greater than it's numbers would indicate on paper. And that is due in large part for the simple fact that it's easy to shoot and folks tend to be very accurate with it. Always amazing to me when in the field folks find that I am hunting deer or elk with a .375H&H and invariably if they aren't in the know will comment about using an "elephant" rifle for poor little old elk. Of course the same is not said about a .338 WM which puts out just about the same muzzle energy with a 20 gr lighter bullet at the same velocity as my 270 gr load and it does so with .037 less muzzle diameter? For all intensive purposes the same power level capable of all the same things that the ole H&H is the only difference being perception as Capstick wrote about the .375H&H and not the .338 WM.
The .375H&H is a fairly mild round to shoot and even with expanding rounds does less meat damage than a super velocity light round does. The .375H&H does what it's been doing well for over 100 years now it provides just enough power and penetration on heavy game and performs like a champ on everything else. I've killed multiple hundreds of head of game with a .375H&H from coyotes to cape buffalo the majority of shear numbers being feral hogs but a good amount of my elk and caribou and stuff like that were with a .375H&H and I've never once found the H&H to lacking in any way especially in the meat damage department. My go to load is a 270 gr TSX @ about 2700 FPS. It simply does not tear up meat.
I've poked multiple hogs and other light stuff like wildebeest in addition to elephant and buffalo with my .470 NE and my .458 Lott, again it simply does not tear up meat like say a .300 mag or a 7MM tends to. Nice clean entry and exit holes and that is with expanding bullets these big rounds simply zip through light animals and don't transfer a lot of energy leaving minimal damage. The same can be said for all of the heavy and medium rounds I've mentioned above.
Here is the one and only thing that I will caution about using heavies on light game. BEWARE of what's behind the animal these big heavy rounds will over penetrate and they carry a LONG way after sailing through a critter, they don't act like your "average" deer rounds. I just about killed a hunting partner one time with my .470. I didn't know that he was up the same draw I was working. I jumped a hog and shot him in the rear as he ran off. The 500 gr Barnes went all the way trough the hog lengthwise exited the neck hit the ground and I heard it whine off into the nether lands of Western Texas.
My buddy was about 200 yards up the draw and told me later that he heard me shoot and then heard what sounded like a buzz saw go flying by, very close to his head. It was my "spent" expanded bullet zinging away that went by. Y'all be careful out there playing with these heavy rifles.