Gal Civ is to space sims what vanilla is to ice cream. Standard, bland, inoffensive.
I adore Gal Civ 2 and will defend the gold edition (or whatever that's called) to the death. It *should* be like you describe but its not, its this weird mix of playfully making fun of its own genericness, and a whole-hearted embrace of everything that defines Star Trek. I can't really describe it, but Civilizations tends to follow a pretty predictable course, like a few civs hopefully including you are going to get powerful and then people are going to DoW each other at random, that's about it. Galactic Civilizations 2 has this way were you think it will settle into a boring economy fest or easy victory but then somehow it will always surprise you or tell you an interesting story. The fact that it oozes character especially with the expansion that gives ever race its own tech tree, well so much the better.
For example I had one game where I replaced all the races with Mass Effect ones (not even modding really, just drag and drop image files the rest can be done in-game). I was playing as the Quarians, with the rest of the races being more belligerent ones like the Krogan and Turians, and of course the Geth. The idea being that the Quarians live in a fundamentally hostile galaxy and I wanted to represent that. What actually ended up happening however is that the Turians attacked me because my military was so much weaker than them, so I bribed the Krogan to attack them and then spent half the game in a slow grindfest of a 3 way war desperately hanging on. In the end everyone despised me except a distant neighbor I had done nothing to offend... the Geth. And thanks to the spiteful stalemate I maintained in my losing war they became vastly powerful and began conquering the entire galaxy. I managed to somehow eke out an alliance with them and then I aggressively took every planet from my remaining enemies because if peace happened the Geth controlled so much they would win an influence victory instead of us both winning a diplomatic victory. In the end the Geth reconciled with their creators and allowed them to remain independent out of what I can only presume is a kind of nostalgic fondness, because they certainly could have wiped the Quarians out.
That's not even getting into the silliness that can happen if you have the expansion that adds mega-events. I've had some real interesting games with those (most of them are designed to effect all civs equally, like splitting every civ into two splinter groups at war with each other or turning a huge chunk of the galaxy into low-quality habitable worlds and causing a second colony rush).
All that being said it is in old game, it aged well but its been like a decade at this point. I've never seen the point of Galactic Civs 3, at first the reviews were like "maybe it'll be more fun than 2 with some expansions" but then I've never heard any convincing evidence that it did become more fun.