A very short list of things new to Gal Civ 3.
1. Buildings new have an adjacency system where most buildings give bonuses to buildings of certain other categories place next to them. This makes placement of buildings on planets vitally different.
2. Economy is now population based on money based. In Gal Civ 2, science and industry buildings converted money into other resources. It's entirely different now.
4. Completely revamped system for the races and a really great custom race building system.
5. Unique resources required for building things ala Civ V. Unlike Civ V, you can make do without them, but really powerful components/buildings require them.
6. Choosing your affinity through the event choices now allows you to unlock perks. These are actually pretty powerful, so being good, evil, or neutral can make a big difference.
7. While they aren't quite there yet for all races, some of the traits really give the races given them a unique feel, especially the Yor and their total lack of food or population growth, and the DLC Snathi and their ability to salvage ships.
8. The underlying engine is all new and very solid. Harder to appreciate that, but it is a big thing.
9. Due to 9 above, you can now make an epic sized galaxy with 100 different races flying around in it. Not for the feint of heart though.
10. Tech trees now feature Specializations, techs with 3 different versions that each unlock different permanent empire wide bonuses, but you can only choose 1.
11. None of this research 5 different versions of the same weapon nonsense from Gal Civ 2. Tech trees have a lot more variety now.
12. Ship production is no longer planet based. Instead you building shipyards that sit in space and draw production from nearby planets of your choice. Closer planets a more efficient in their production transfers. You can move the shipyards around. Since they can't have defenses other than ships, they become very important in war time for both sides.
There are other things but I can't remember them off the top of my head.
In general, while much will be familiar, it's a very different experience for me.
Here's an official link on the subject http://forums.galciv3.com/463709
Also in the future they are planning on adding an espionage system, a new trading market that sounds similar to the one from Endless Legend, and a few other redone things. These are for the base game, although their development is funded from DLC sales. You won't have to buy the DLCs to get them though.