A rim around the edge of the pot is brilliant. I've had pots of water fall off my cooking set up on three occasions. I no longer use beer can pots for that reason although I know there are some set ups that are fine.
The old Camping Gaz GT106 stoves had an upturn on the end of the pot supports, which was also brilliant but did limit the size of the pot that one could use.
Pot stability is generally pretty subjective. That said, I found that the number of supports mattered. In general, stoves with four supports had better pot stability with larger pots than those with three. The GS-100 has the shortest pot supports of any of the small gas stoves I tried, but I found that it had excellent pot stability.
Adventures In Stoving