I really like it, despite its flaws. To get the worst out of the way first:
1. Lots of DLC, and without it the game does feel bare. I recommend getting at least Leviathans and Utopia, but everyone has their opinion on this.
2. The AI is... hit and miss. Supposedly the update to 2.0 broke some of the AI's understanding of warfare, and there are known problems that haven't been fixed. It tends to fall behind economically as well, but you can increase the difficulty and its artificial crutch to help with that if you care.
3. If you get very far ahead of the AI, the game can get boring since it's not suicidal and won't usually attack if it doesn't think it can win. I have yet to have the AI declare war on me in about 175 hours of gameplay, and since I RP as pacifists I don't declare war in turn...
Overall, I think "broad but shallow" isn't a bad description. There are planned improvements (read: new DLCs...) that will add more depth to the economy and diplomacy, but we'll have to wait to see how they turn out.
Still, I do greatly enjoy the game. Maybe I have simple tastes, since I can still enjoy the micro of expanding a space empire peacefully and checking off new technologies that are researched. The game does spice it up some in the "end game crisis" though, which was a lot of fun for me the first time it happened. I'd thoroughly beaten the rest of the galaxy through economics and technology alone, but when that rolled around I thought I was going to lose. Prior to the crisis, I had a long and tense relationship with my neighbors, who hated my guts because they were self-proclaimed democratic crusaders and I was playing as authoritarians. The game does have an emergent story feel to it, but you do have to fill in gaps yourself.
For me, one of the more appealing features, after I got it to work anyway, was the ability to do portrait mods so I could play as whatever I wanted. I've played through a few times as authoritarian, pacifist and materialist sapient horse-deer-things, and am now playing through as authoritarian, militarist and materialist space dragons by lifting some recolored Spyro character portraits. My brother said that was a very noobish thing to do, but I don't care, I've got space dragons now.
Worth mentioning that there are also tons and tons of mods for the game, if you like that, but you can't get achievements if you use them.