I have no experience in the matter, but of course I do have an opinion.
No matter which species you are talking about, I would consider the .308 to be on the light side for an animal of that size. There is no doubt what so ever in my mind that a .308 is capable of killing a buffalo, bison, or water buffalo; and killing it humanely. However, the problem we run into is, what if you don't have a picture perfect shot ? Picture perfect meaning, the animal standing broadside to you and not moving where you need the least amount of penetration and have the maximum chance of placing the bullet precisely where it needs to go. If the bullet hits a heavy bone, or the animal is angled away from you .................................. it may not be up to the task.
If you are talking African Cape Buffalo, then no, the .308 Winchester is not adequte and I dont' think it is even legal. With large dangerous game animals your goal is to "break the animal down". A bullet hitting the animal anywhere but in the CNS will take some amount of time to kill it. It may be very quick, but it will take some amount of time. So, you shoot to try to break major bones that would incapacitate the animal so he can not "get you" while he is dying. An example might be a shot through both front shoulders. I wouldn't want to count on a .308 to accomplish that. I wouldn't trust expanding bullets for that and I don't even know if I would trust a .45/70 for that although I would be much happier with a .45/70 than I would a .308,
Disclaimer: This is all based on stuff I have read and may be total BS.