Craig Boddington has shot a pile of buffalo, and after a while wrote that he found the standard behind-the-shoulder, double-lung shot used on deer as effective as any. In fact he's killed several with a 300-grain .375 Sierra GameKing, placed just behind the shoulder, just like most hunters would shoot a whitetail. And no, he did not write that to promote Sierras as the perfect buffalo bullet.
But many PH's still suggest a low "shoulder" shot, to break the big bones, which usually means a heart shot--but I suspect that's a holdover from the days when solids were commonly advised: Breaking bones meant a more inside damage, due to "bone shrapnel."
But today's deep-penetrating expanding bullets make a big hole through both lungs, and kill pretty quickly. However, that's only if, (as an old elk hunter once advised) you "give them time to die." Buffalo are big animals, and like elk and, especiallu, moose it takes a while for the lungs to fill and collapse.
The tendency is to shoot any buffalo as long as it's standing, which is smart. But a second shot (or third, fourth, etc.) tends to get them moving again.
The first bullet I ever fired into a buffalo was a .375, 300-grain Fail Safe, a bullet that expanded and penetrated exactly like a Barnes TSX. I aimed at the shoulder, but the buffalo stepped forward at the shot so the bullet landed just behind the shoulder. The PH and I shot three more rounds, but the bullet that did the job was the first Fail fafe, which left an exit hole the size of my fist. That bull went around 60 yards before stopping and, a few second later, collapsing.
