I see what your saying. Although, they are adjacent Orders, so I think they'll actually be more similar than not.
I think what's going to determine which laws Skybreakers have to uphold is going to be some combination between which legal systems longstanding enough to have their own cognitive aspects, and what laws are actually "just". For example, say in Shinovar it has been illegal for a millennium to make fun of someone's shoes. If this law had been culturally and mentally ingrained in the society, then, at least while he/she is there, a Skybreaker would be required to follow this law because the law itself would exist Cognitively. Conversely, a law that requires you to immediately kill someone because they tripped, would probably go against the greater ideal of Justice, not requiring the Skybreaker to follow it. Or maybe if a government makes a law outside its statutory authority (like Congress making a law to censor free speech), since this new law is technically illegal, the Skybreakers don't have to follow it. The divine attribute is Justice, and not Legality, after all. I'm betting their third ideal will do something to clear this up some.