Personally, I find that Distant Worlds: Universe to be the most authentic space 4X experience. The absolutely greatest thing about it is that you can feel that the galaxy is alive, it is enjoyable even just to watch it as an ant farm. There is very little if any artificial gameplay feeling, everything just feels organic. Space stations occur naturally, patrols and pirates do their own things, civilian ships transport their own goods and earn their own money. The game's presentation is serviceable, but still bad, with terrible font and just a very weird style of art direction.
I have recently played both Stellaris and Endless Space 2, and the comparison is quite interesting. Stellaris early game is ok, but mid-late game is quite bland unless you are in constant war or a crisis happens. There is very little to do or even to think about other than research, colonize, build stuff, research, repeat, which is in stark contrast with other Paradox games.
I have played ES2 only for like 10 hours; it has far better fluff and gorgeous shit to look at/listen to and have more events, but the galaxy itself compared to both games above feel both tiny and restricted. Also colonizing planets is also far too easy to do with 90% of the colonizing tech reachable within 50 turns; the side effect of this is that it makes most planetary systems (and in turn the galaxy in general) lack personality because you can literally colonize everything. I prefer Stellaris with how terraforming is a very lenghty and resource consuming process, and habitable planets are not easy to come by. Combined with how different species can live on different environments for better or worse, it makes the universe feel like a real spacefaring experience.
Other older space 4x games:
- Aside from the fact that it's so combat focused that it feels like an explore, expand, exploit, EXTERMINATE game, Sword of the Stars is decent with excellent ship customization system that actually matters, and demands better strategic thinking. It is good if you are in a mood of some space Total War gaming, but there is nothing memorable at all regarding its peaceful gameplay. I have never played the 2nd game.
- Sins of the Solar Empire IMO has the best presentation and the slickest control......probably because it is played like a RTS, like a Homeworld game with more 4X elements implemented into it. It's definitely not a game that I could sit down and play for 30+ hours.
- AI War is weird, but good. It doesn't even have diplomacy, and it's extremely combat focused. But it has great exploration with lots of interesting stuff do discover and use, and has dynamic emergent gameplay. Even a single game can be very long but the game keeps you on your toes due to how it changes it difficulty as you progress. The 2D sprites here are better than DW:U but YMMV.
- MoO2 is classic. I haven't had the luck to play it when there was not a lot of space 4X around; I played it too late in my life, so the magic of it didn't have such a big impact on me.
In my opinion, all these space 4X games more or less suffer from one problem: the presentation (or lack thereof) of a mysterious galaxy. You know that feeling when you play Elite, Star Control 2, Mass Effect 1...and the joy of going into FTL, changing into a new ship/getting new crews/toys, visiting new planets, discovering new biomes/cultures/aliens/ancient ruins for the first time? It's unfortunate that for most space 4X games, despite that you have a whole fucking galaxy with hundreds if not a thousands of stars for you to design around, there is often not a lot of excitement to have. A planet with some strategic resource? Cool, there are many others. Wow this one has an anomaly! Bleh, just some extra research point/money/minerals. Undiscovered alien species! Turns out to be just another extra mini-farm for resources.
Seriously, why can we discover anomalies/ancient ruins/strange species only for ONE single time per planet in almost all space 4X games? It's like, if an alien ship scans Earth and has discovered only the Pyramids, and that becomes the one and only "Unique Resource" of Earth which provides +3 Influence/turn or something.