I decided to put my feedback for the Retribution expansion here.
What I'm playing is probably relevant. I'm playing GalCiv 3 from GOG. I have the Crusade and Retribution DLCs installed.
Hyper Gates.
I thought I would like hyper gates more. I've used them a few times, but I've found that I rather save administrators than use them. However, I'm quite happy to use the hyper gates my enemy builds.
In practice, I don't need the speed boost. I like to form big fleets so what slows me down is ship production. If I can help it, I won't send a fleet to the front lines until they are ready to overwhelm the enemy. Once my fleet reaches the front lines, they stay there until its time to recycle them. So there is very little moving back and forth using hyper gates.
I found that hyper gates are dangerous to my troop transports. I've had enemy ships pop in out of nowhere and kill my transports by using hyper gates. I can usually keep my transports a safe distance away, but hyper gates changes that. I'm finding that making my transports avoid hyper lanes is a good idea.
I play on smaller maps. I'm not sure if that plays a factor in my experience. For all I know, a bigger universe might make ship speed a much bigger deal.
Supply ships.
I like them, but I haven't been using them as much as I might like. Early on when they could be useful for developing my worlds, they are competing with my colony and constructor ships for production. By the time I'm finished racing for worlds and resources, many of my worlds already have a space elevator, a shipyard, and a few factories. Thats half the planet development battle.
Supply ships are very expensive. The supply ship costs about 230, while a colony ship can cost 40 or less. It is a lot more economical to build a few colony ships than a supply ship.
I have sent some supply ships to planets that are building aid research or train legion. I find it is quite expensive.
Artifacts.
I haven't been using them much. Maybe its just me. I haven't been needing them to win. I'll make a point to try to use them in my next few games.
Other.
I haven't been liking the changes to make a bunch new of 1-per-player planet improvements, and turning existing planet improvements into 1-per-player improvements. For example, a military academy is now a 1-per-player improvement, therefore only 1 world can train troops. A deep core mine that can only be built on 1 planet is madness.
We don't seem to have top tier sensors techs any more. Some of my ship designs can be made in the ship designer, but I can never able to use them in play cause I can't research the required techs. They are gone.
Being able to repeat aid economy is a god send.
I found it really annoying having almost no things to build on my worlds when the game begins. Building factories shouldn't a hard concept. I have to do research before I can build the basics, let alone anything fancy.