This is a great explanation except for one detail. Stability refers to release cycles in the Linux world, so your description of stability is a little redundant. The word you're looking for is reliability, but all 3 of the giants provide that.

The release cycle and the package managers are the two biggest factors that most people decide their distro based off. There are some more considerations as you get deeper into the Linux world, like your init system and whatnot, but those two are the big drivers IME.