Thoughts:
Hmmm...so I'm having a lot of fun but the game is definitely best at the beginning when it's feasible to manage everything, you're upgrading your ships, exploring, your rivals still pose a threat, etc.
I played a really peaceful civilization my first time and just had a really lucky starting point that allowed my empire to get huge all while I was never invaded, and diplomacy just sort of happened around me.
This non-interaction led me to restart as a similar civilization and I found myself locked into a tight start with rivals immediately surrounding me and more powerful rivals just beyond them. I staked out a decent territory and built my civilization and tried to be more engaged in diplomacy. Then the guys I was courting were conquered by my neighbors so I ended up deciding to carve out allies by force, through "liberate" war goals. This got me friends but it also angered everyone around me and when my friends decided to declare their own wars of expansion on the back of my fleets, I was the one who was invaded from all sides. A lot of tactical retreats and ganging up on smaller forces put that to an end but it was pretty crazy for a while and soured me on my alliance

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So, next I decided to play an insect "hive" society that didn't respect other life forms and enslaved the drones of its own species. I managed to dominate and incoporate my nearest rivals over time, colonized agressively, etc. and now that empire is huge and there really is no one who can stand up to it at all. A fallen empire invaded to teach me a lesson and I ended up enslaving them. I miss the times when, say, the preythorians invaded and they scared the crap out of me requiring that I scramble every ship I had as I was making them.
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I like a lot of the systems in the game and they are quite detailed but I wish there was more variety. When I first started learning psychic technologies on my first game I thought it was perhaps special to my government type, species traits, or something and that the game would be very varied. I was disappointed to run into the same technologies on my insect race although jump drive is an extreme blessing. The same thing with events--I got some pretty neat and new ones on my latest attempt but so many of them are just the same all the time. I always wonder if it's just that I play too similarly every time, but all the minor aliens lose their appeal when they're on every map. Also, I wish the game wouldn't recycle planet names so much

. At least use II+ so I stop getting confused at which planet is being brought to my attention.
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Influence is strange and it is weird that you can just 'hide' frontier outposts in sectors. I also wish the leader system was reworked a bit, maybe with limits for different sorts of leaders rather than a general limit. I found myself never using, say, a general and using a lot of room on sector governors, especially in my huge insect empire.
Power is an extremely finicky resource in the early game, competing with your expansion, science, and military power. Even in middle game a war is disastrous to it with the fleets undocked, but when you can have multiple 20k fleets out and about and be at 5k power with +150 or so a month, it has become completely meaningless.
Metals are less hard to get going but you have to use a lot of them to build your stuff so until you are sitting on a complete core sector and just grinding science, colony ships, and ship reinforcements, the resource sees healthy depletion.
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I find diplomacy disappointing, but I also haven't had much luck with it. In general, people outside your alliance seem unwilling to do most everything with you besides trade metals and power or maps. I ran into too many "-1000: You can't do anything to change my mind even though I like you scenarios."
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I like designing the ships but I wish there was a better way to test your armaments effectiveness and balance. Let me do tests on dummies with varying shield and hull strengths to see if my armament is well built or horribly lopsided. Also, I'm very unclear on how squadrons work. Is their 8 range from their mother ship or from when they're in flight? If the latter, how far afield can they go? If the former, do they do much more than defend the ship? Seems that'd be a strange version of carrier warfare.
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I already like the support this game is getting, with scourge worlds being destructible now and the ship building screen more organized. The things I want the most are improvements to technology, diplomacy, and bureaucracy. I've had a few bugs like being told I lost a planet when I reclaimed it with my armies or losing armies on an a now-vassal world after peace talks with them still being on my budget.
Generally, the game has a lot of content and a lot of depth but not in quite the right way in the core areas, imo. I've been quite addicted to it, and like it a lot though.