reaches into the closet and dons the old but comfy roleplaying hat
It is hard to go by roleplaying alignments for each of the outfits. They can all use kidnappin or This is a Holdup, so none fit into the "good" portion. Technically, I would define the law dogs as something more along the lines of neutral good (bending the laws when necessary for the greater good) at best and lawful neutral (using the rules to get what they want) at worst.
Perhaps the quickest way to describe the factions is by stating a couple of keywords that are used by many of the outfits' dudes.
Lawdogs - punishing cheaters and blessed (buffing) magic.
Fourth ring - abominations, huckster (attack/control) magic.
Morgan - ranches, horses and gadgets.
This isn't an exhaustive list, but it might be a way to quickly convey flavor.