I think it's all down to personal preference really, and more to do with that than anything regarding which cartridges we choose, with specific cases as exceptions.
As shooters we try many many different guns and loads over the course of our shooting lives, and some ( by more to do with luck than good management ) happen upon a cartridge and gun with which they experience superb results, and regardless of shot size or weight of charge, nor recommendations from other shooters, they stick with.
There are two for me, the first of which is Gamebore Clear Pigeon 30grm 6's. I discovered these many moons ago and found they were the best all round cartridge through my Winchester 101's for ferreting bunnies to guns. They will bowl over those rabbits no problem whatsoever, even going away ones. In the past I have shot some unforgettable pheasants with these, and they are my go to cartridge in the hide. I am never without these.
The second is SIPE 32grm 5's which I now shoot game with exclusively throughout the season. I can't recall why I initially tried these cartridges, but after having great success with them on a shoot, and realising I was going to need something a bit punchy on last seasons beaters day I decided to use them in my Gamba and I had my best ever days shooting. I've used them throughout this season and they are the dogs danglies for me, they just fold up stuff in the air.
Saying all this, most foxes on driven bird days are killed with shot size 6, although it isn't ideal as sometimes a follow up is needed, and if you put that pattern where it matters, within accepted parameters, any cartridge will do the job. People shoot game with .410's.