I've played a few games of various sizes and difficulty levels. I have a couple of observations, and I apologize in advance if one or more of these issues has been raised; I just don't have time ATM to keep up with this thread:
1. I still think the game needs the ability to increase game speed, the game still plays too slowly, IMO.
2. While I appreciate the improved AI, There are some things that need to be tweaked. For example, if there is a safe passage between two systems, trade systems and resource ships should never, ever, go through hostile territory (regardless of jumps). If there is no safe route, then that's a different story. As another example, there have been instances where a computer controlled fleet just hyperjumps back and forth between their system and my system. Once they reach my system, it appears as if they realize they can't win, turn around and run. However, over time I am able to whittle them down with my system's defenses. The AI should do exactly what a player would do in that situation. Wait and attack with superior strength.
3. Related to #1/#2, the game is still too easy

(I apologize if I am sounding like a broken record). I have played numerous games in a small galaxy (one star) with all 10 empires on hard and had no problems methodically defeating all of my opponents. The only thing I have yet to try is a small galaxy where the other 9 AI opponents are locked and allied against me. I'm not sure what I would do remedy this issue, but I think the AI needs to attack in greater strength. It seems to me that they just break themselves against the defenses of one or more systems and leave themselves wide open for counter-attacks from my fleets.
4. I like the addition of the military research base/civilian research base. However, I think one thing you could potentially do to improve the strategic importance of having more than a certain number for a specific level of technology is to provide passive bonuses (beyond the build speed increases; the speed increases do not seem to really be that important). Maybe each tech level (and beyond) comes with its own passive ability that is unlocked once the appropriate number of labs are constructed. The passive abilities should increase in power, so that there is reason to build X labs, even if a particular tier of research doesn't include anything that the player might normally research. For example, on the civilian path, I usually only build 5 labs to get the resource station, the rest of the civilian tech is researched much later in the game as a luxury. None of them are central to my strategies.
5. I like the new artifact/exploration system. You'll have to excuse the ignorance, since I have never found the need to research it (and once I have the extra resources there just doesn't seem to be a need), but do the probes that can be research for the scout frigate allow any sort of exploration to occur? Perhaps to give them additional strategic importance, if they are used on a planet, they can explore 50% of the planet automatically...
6. I also agree with some other people here; I think a ships overall effectiveness should be related to its overall health. If a ship has only 50% of its hull points, then all of it's parameters should be lowered by an appropriate amount. I'm not sure what that should be, but perhaps that can differ from ship to ship. For example, a Kol is designed for battle and as such should probably have redundant systems. Maybe more than 25% of the ship needs to be destroyed before it looses effectiveness. Also, it might be interesting to allow fighters, bombers, and possibly frigates to target subsystems. Nothing too complicated, but maybe a target engines, or a target weapons setting, which could be combined with the above system to more quickly reduce certain types of ship effectiveness more quickly.
I guess that's it for now. I'm probably going to give the 9 on 1 a shot and see if that is any sort of challenge... Thanks for listening.