I'm sure you will get a few replies to this post!
I was hunting alongside my son on a recent water buffalo cull hunt in Australia we were sharing a double rifle in .500/416NE (Rimmed .416 Rigby) and a .375 H&H Mag bolt rifle. We were shooting 400 gr bullets in the .416 & 300 gr bullets in the .375. We shot a total of 32 buffalo in 6 days hunting.
There was a significant difference in the effectiveness of the 400 gr .416 compared to the 300 gr .375. I'm not saying that a .375 is not capable because that would be a stupid comment but I am saying that a .416 is a much more effective choice.
My experience on this trip convinced me that I needed a .416 bolt action rifle for future buffalo hunting trips. I just got out to shoot my new Blaser R8 in .416 Rem last week, I could not be happier with it's initial use, it's super accurate and achieved great grouping with 400 gr ammo. It will be my new standard go to rifle for future buffalo hunts.