Hello Speedy O,
I do not think government type or economic type changes missions as such. A Fed Democracy is just as likely to order an assassination of a clean target as an independent dictatorship (hmm, showing my colours there!).
Relative influence affects who's missions appear, and state affects what.
Certainly prior to 1.4 there was a trend in mission types based on influence percentage of faction and their state, or it at least seemed so to me, some of these also occur with pending states:
1) Boom : more trade missions and take documents for signing. (to increase boom or produce bust)for some reason from the system in question.
2) Bust: More charity missions.
3) Lockdown: Kill x piarates (tends to be from other systems into the system, rarer apparently in 1.5).
4) Civil Disorder: Assassination missions (there is a kill the leaders of the rebellion titles one) which reduces civil disorder as well as upping influence.
5) non station controlling factions will tend to give smuggling missions (take X illegal ), and try to compete on the trade routes (take X legal) with the controller.
This is about all I spotted, and very much prior to 1.5 - so many not work the same way in 1.5. But I guess the gut of my post would be relative influence/control of station/state give a good indicator of hoe shady and sort of missions. I do not think anyone has tracked mission and outcomes, let alone state and mission occurrence.
Hope this helps (a bit).
Simon