Sorry, ignore my previous post as I accidentally hit enter and was going to edit it but now I can't, and if a mod could delete it that would be nice.
DISCLAIMER: I've only played GCII, without any expansions at a friends house a few years ago (more than once) so sorry if any of these suggestions are already in the game.
I think GCIII should adopt the engine used for SOASE, maybe expand on the graphics where needed (explosions for example), but allow the optional "classic ui/graphics" so people don't get disappointed because their favorite game of old looks different. A 3D map like in EVE Online would be great but with the ability to switch to 3D...
The five other really big things I want in GCIII is, and am looking for in any spaced based rts, but more specifically the GC series:
The ability to take over a battle and control it in real time, imagine how much more you would sell Stardock, if any higher ups are reading this, if you gave players the ability to micromanage battles and use their own tactics, and maybe have aliens use their own manuevering tactics, maybe totally far out bizarre battle movements that make the races seem utterly alien that the player has to adapt to, this would really sell GCIII to the people like me who are casual fans of turn based games but really love RTSes but want deep strategy at the same time.
I also think major figures would be a good addition, like maybe a king, or a president or a warlord or an oligarchy of politicians, all could be named and have personalities, scandals (drug addictions, alien scandals) and traits. And then lesser figures like famous generals who earn their way to rank from battles, or maybe get statuses handed to them because of a royal connection. The player could attempt to create propaganda, with the possibility of the truth getting around and other factors that impact the leader's popularity.
I would also like ground battles and planets to be fleshed out both in graphics and options, such as micromanagement over armies, let's say you want to take over the food production plant, you could go into a real time mode and siege the facility for example and then the populations nearby would suffer, or what if you could call in fighters and possibly other ships from orbit? I think you should also be able to see a graphical representation of different cities and their inhabitants, like possibly being able to see parades at a terran diplomacy meeting, or a brutal drengin display of power and cruelty to foreigners and the ability to change the architectural style.
Back in the bigger scale of things, there should be different disasters to make a race more flawed and more believable, like maybe overpopulation issues (Mote In God's Eye anyone?

), famine, plague, ect and a united race, dividing into factions, maybe even on a sub planetary level.
Lastly to increase immersivenes players could follow a named ship with named characters through its exploits with fellow members of their race or first contacts with aliens, even with events occuring between crewmen, mutiny ect and these being logged in a journal players can upload to share sort of a space drama with other people, or maybe a charter of rulers where the major events get logged in and the ability for the player to create stories about them and other things.
For those of you who can't be arsed to read all of that I think the biggest things for me would be:
1. SoaSE graphics engine but the ability for a "classic" ui or engine.
2. Real time battles.
3. Planetary interaction fleshed out.
4. Named figures in the empire.
5. More immersiveness.
6. Adding the best features of SoaSE to help create a game that caters to a wider audience.
Sorry if I ranted too much...