First of all it is critical to understand that the game is still in beta testing and therefore has some glitches. That said it has been pretty stable for me. (Four year old dell xps 8100 with 16gb and a 750 Ti video card). At present the plan seems to be to a go for a final release in May. There will be frequent patches before then and perhaps a beta 6 release (beta 5, with enormous additions, was released yesterday (Mar26). If you don't like encountering bugs and reporting them to help the game, then wait for the release. Of critical importance remaining is tuning the AI to be smarter and more aggressive, imo.
That said, with yesterday's release the game is really starting to take shape. I played and enjoyed Galciv2 (for which, coincidentally, a community update is being finished at the same time). But GC3, even a couple of releases ago, just looks so much better, and the game will optionally be so much bigger (largest size is "insane" and it is just that, largest number of factions...100!) with many more custom races allowed, more minor races and a much improved ship designer (which is a game in itself that one can get lost in). Colonizing of planets is more tactical with the new adjacency bonuses and on planet resources. The battle viewer will remain a strategic choice rather than a tactical (one can organize one's fleet with different numbers and classes of ships, of which support ships are critical) but it also looks much better than GC2. You can change camera viewing angle during the battle. Watch a 30 vs 30 ship battle, enough said (check stardock.com
to see live stream game examples). Then there are various galactic items like nebulae which restrict defence and accuracy as well as numerous strategic resouces to mine in addition to relics that give civilization wide benefits. The ideology table gives some sharply different choices depending on whether you feel good, bad, or neutral. Diplomacy is rapidly improving but has some way to go (as I said) and will I think be a key to success in a big game.
Well, I could to on and on. I am a long term 4x player (started with civ 1 in the day) and my advice is that this game will give a 4x challenge that feels, looks, and plays much different from, say, Civ 5, but with the same next turn tension and the same scramble for multiple objectives that makes a 4x game enjoyable.