With today's super-tough "premium" type, bullets, I strongly suspect the .375 would let the air out of the largest, toughest buffalo that exists (as it has been doing very consistently these days).
Regarding premium bullets, I'm definitely +1 with johnnyblues on the Swift A-Frame.
If I were using a .375 on buffalo, I'd load the rifle with a 300 grain A-Frame as my first shot.
Likewise, I'd load flat nose solids in the magazine, in case of a follow-up.
That's of course if follow-up is even needed.
My prediction however, is that you will fire your all important first shot into just the right spot on your buffalo and he, although mortally wounded, will turn to run away.
You will have practiced mightily for this scenario and so, you then will fire your 2nd shot into him, from caboose to engine and he will crumple before you can run the bolt for a third shot.
Grab that Winchester quick! Fill it with Barnes 350g TSX and you have a one shot kill machine for buff. I took mine with that combo last year. A head on shot. He went about 80 yards and we found him stone dead. I wanted the slug and the skinners went through every inch of that critter and never did find it. The PH guessed it went clear through stem to stern as his butt was a mess.
I load my 350g Barnes TSX with 52.8 g of 4064 for 2257 fps and 3960 ft/lb energy. My 235g Barnes TSXs get 43g of 4064 for about 2400 fps and 3400 ft/lp energy. The 350s were devastating on buff and the 235s got one shot kills on PG.
Greetings all! I've been a hunter for 50 years, but only now planning a trip to Africa. I was fortunate and successfully bid on a couple hunts for plains game in SA later this year and next. Also a rare Native Texas (5th generation) and USMC Vet. Hunt safe y'all!