A friend of mine heart shot two big water buffalo bulls with his "new"-vintage Mannlicher Schoenauer in 6.5x54. Used a Barnes X in 140 gr I believe.

He knew exactly where to place the bullet on the broadside animals at fairly close range.

With the first bull he was urged to shoot it again a second time and the bull ran but fell dead some distance away.

With the second bull he ignored the panicky demands for a second shot, the bull walked as if not shot at all and dropped dead after a few steps.

Medium calibre rifles will no doubt kill buffalo, but are not adequate for the small number of cases when a bull gets toeey ie no knockdown power. Same for if the bull runs away with a less than spot on shot.

All of the buffalo I have shot have been shot with my 9.3 or .450.

A .444 Marlin with the right bullets would probably work similar to a .45/70 with the right bullets. Not deer/soft bullets.

A .30-06/.300 etc with heavy bullets eg 200 - 220 gr - would probably work OK. A .338 would be better with a 250 gr bullet or heavier.

Using sub-standard/medium calibres can kill anything on Earth but the placement becomes more important, and the willingness to forgo shots etc.

As Ben says, many Aussies claim medium calibres are all that is needed. But they often forget to tell that they are shooting from a vehicle. Or if an animal runs away, their attitude of "WGAF" is also relevant and needs to be taken into account. The professional outfitters almost all recommend a .375 or similar as a minimum.