As far as space games go, I thought GC2 had a ton more personality and told things on a more intimate level, also it's very possible to design and name your ships following a certain theme in order to create a bit of atmosphere for yourself.
Sometimes I try to bear in mind a basic mindset of the race I'm playing, and make that a factor in various decisions, I'm not that great at juggling the numbers anyway so choosing based on my idea of what my people would do is just as well and adds a lot of spice to the proceedings. Sometimes they'll be xenophobic and haughty, and take an aggressive stance to all other races; sometimes they'll be eager to form alliances and only maintain a meager military in times of peace. Some empires will build influence starbases to counter influence rushing, while others will go to war and make the interlopers pay dearly for their insolence.
My point is a lot of the atmosphere depends on you, the player, which lets you define that atmosphere however you wish, but of course that doesn't really do it for everyone. I think the expansion pack will add more flavor to the game, the only feature I've heard of so far in the expansion back is a text breakdown of what happened during the game, kind of an end-game narrative. Perhaps they'll do something to give you a more solid narrative during the game too -- the AI's pretty good at figuring out the situation and the balance of power and interpreting things (all those descriptive diplomacy messages we get), maybe they can offshoot from that a 'storyteller' AI that determines what's going on and figures out story or even game consequences as a result. Perhaps random events will be more common, but less random, effected by what's going on in the game?