No.
Every minor-faction is the same. The missions are the same. Only the names change. Maybe someday we will get missions based on major faction, government type and other aspects of the minor-factions giving the missions.
Until that day - everybody is evil.
^^ This indeed
Apart from Unfettered/Freeman Factions doing increased Piracy with relaxed Commoditiy rules and Democracies prefering an Election over Civil War - no differences remain outside of Empire Factions having Imperial Slaves in their trade portofolio.
Thus, whatever faction or government you support...
You're essentially working for : {String}
100% replacable, generic and arbitrary, no matter where you go.
So pick your favorite and support them.
But what kind of a difference will this make? None.
It's absolutely irrelevant.
It really boils down to making up your own RolePlay, because only in your own mind you'll be able to create those missing differences.
For the time being... That unfettered Faction sitting in Archon Delaine's HQ System basically acts almost
exactly like the Pilots Federation in the Founders world (who supposedly represent the law).
Both will happily offer Missions to terrorize Civilans/Traders or kill Authority even from their own Faction in the next-door System and shower you with Credits and Reputation for doing their bidding.
So will both the Federation and Empire Navy for any rank progression.
That's the sad condition of the core game as we speak and no improvement is in sight.
At least in my Opinion, likely the largest and most critical oversight/bug in the entire Game.