I guess I will add my opinions on the matter.
First of all, I would like to say that both Sins of a Solar Empire and GalCiv II are among the best games I've ever played! Kudos for Stardock for creating such great games. So, here's what I think would make the game better:
-Dynamic Map: Other than asteroids and the occasional anomaly, the map is basically just a passive background in which stuff happens. I think the map should be made a little more dynamic, such as having black holes, or having a supernova go off once in a while. As well, certain regions of space can affect the speed of your ships, or the sensor range. Or even combat ability.
-Ability to trade/lease special resources: I like the special resources that give various improvements to your society (e.g. military or economic resource), but, once you "conquer it" with a starbase, I would also want the ability to lease it to another civilization for profit for a certain number or turns. Something similar to what they have in Civilization, where you can trade strategic or luxury resources for a number of turns in return for profit, or other resources, etc.
-Ability to fund terrorism or rebellions: In Sins of a Solar Empire, I liked the fact that you could fund pirates to go out and harass some other empire for you. I think that this feature should be in GalCiv III, except in much more depth. Like, you can use spies to fund pirates (or terrorists, or black markets, or rebellions, etc.). These terrorists could be funded with anything, either with cash or technology, and they would help do your bidding for you.
-Black Markets: There should be black markets, which would have an impact (mostly negative) on your economy. As well, you should be able to either attack it (or support it), and you can even decide to buy stuff from it, like weapons. The size and effectiveness of the black markets would depend on the government style, your economic health, your ethical alignment, and of course the influence of other alien governments.
-Ability to improve effectiveness of the fleet: Sure, one way of doing this is to make your ships more powerful, but there should also be a way to increase the likelihood that they will win the fight. Like, have research options that would allow your ships and fleets to have better tactical ability (like dodging weapons), or better strategic ability (like, they will form certain formations, etc.) As well, you can organize the ships in your fleet to attack in a specific way (e.g. first send out small ships, and then big ships, or something like that).
Those improvements I think would certainly make GalCivIII even more awesome, and make the game more fun and complex at the same time.