well it comes down to a time thing for me (and a storage thing for most.) Using a semi auto, its hard to find brass on the ground, let alone making sure its yours.. At the end of a range trip I have a large zip lock bag full of mixed brass, some mine, some other. All different types of calibers. So I do an initial sorting by caliber then like I mentioned earlier, I have the time and room so I sort by head stamp.
Once I collect a wider supply of brass I'm probably gonna throw the head stamp sorting out the window. Unless there is a specific reason or I feel like being overly organized ( which I often am.) It would be far easier and less time consuming for something like a rifle or revolver. Altho I am a fan of having things organized to the 100th degree. So long as room allows it w/o looking overly cluttered, I will probably sort by head stamp. But for me using an auto loader its solely about organization ( I'm necrotic.)

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sw9ve, 24/7 pro Ds, Hs M4