The primary difference is the same as the difference between rule by a supreme ruler (usually a monarchy) vs. rule by an oligarchy. As portrayed in TNE and in particular in the RC, F-Techs tend to be more benevolent, but aren't always--for example a religious order that uses high tech like magic items. TEDs on the other hand are usually portrayed as bad people who need to be tossed out of power, but aren't always bad people.
In the CoE setting, the Dingirians will work with anyone (TEDs, F-Techs, republics, etc.), so long as they are loyal and aren't too abusive. They are more concerned about maintaining the existing order if it favors them (think British Empire c. 1800s), but aren't above changing it if it does not. The Terrans on the other hand are more likely to land, start converting people to The Faith creating a grass roots organization, then when the time is right, bring in the Marines to help the population "throw off the shackles of tyranny", thus overthrow the existing order and put a Terran governor in place. Of course anything that smells like AI to the Terrans would be shoot first, ask questions later, even if the relationship between the AI and the local humans is benevolent (FYI: the Terran do use AI to kill AI, but the AI they use has been engineered for that purpose, then suicides itself softly).
In the CoE setting, the Dingirians will work with anyone (TEDs, F-Techs, republics, etc.), so long as they are loyal and aren't too abusive. They are more concerned about maintaining the existing order if it favors them (think British Empire c. 1800s), but aren't above changing it if it does not. The Terrans on the other hand are more likely to land, start converting people to The Faith creating a grass roots organization, then when the time is right, bring in the Marines to help the population "throw off the shackles of tyranny", thus overthrow the existing order and put a Terran governor in place. Of course anything that smells like AI to the Terrans would be shoot first, ask questions later, even if the relationship between the AI and the local humans is benevolent (FYI: the Terran do use AI to kill AI, but the AI they use has been engineered for that purpose, then suicides itself softly).