I've played both and I must say this: go for Galactic Civilizations 2, the graphics and gameplay is way better. Not saying that GalCiv 1 is bad, it was a great game, but GC2 is more with the times.
Galactic Civ 2 is basically Civ in space. You start out with one planet and a colony ship and you explore, colonize other planets, meet and deal with other civs, and of course fight wars. The best parts about GC2 are:
1) The ship designer which lets you design not only the functionality of each ship (role, weapons, defenses, equipment, etc) but also the look of it. You can make small scout ships with loads of engines and no weaponry to huge lumbering dreadnoughts bristling with guns and armor. Not only that, but there are 3 different types of weaponry and 3 types of defenses to counter each weapon, adding levels of strategy to ship designs.
2) The AI is far superior to any AI in any TBS game I've ever even heard of. Not only does the AI have its own strategies, but it also observes the player (and other AI of course) and adapts to your strategies (for instance if you make your ships with powerful laser weapons, it will start loading up on shields to defend its ships and start making its ships with weapons that you don't have defenses for). It will also notice you amassing ships near its planets and let you know that it sees what you are doing.
3) The developer, Stardock, is probably the most customer-oriented software developer out there. They not only want to make sure that you are satisfied, they also continue to add to the game with free updates adding features to the game, not just fixing bugs.
4) There is no CD copy protection!!! Once you buy the game, you can install it and throw the CD's away if you want to. You will not need to insert it to play the game, nor will you need them to reinstall as you are able to redownload it as many times as you need. I'm not saying this to encourage piracy of course, as I myself purchased the game. Plus, you need a valid serial number in order to update the game (which v1.11 is pretty much a necessity as it adds so much to the game).
Anyways there is so much more to the game, but those are the major points. I highly recommend it especially if you like TBS games. Just go buy it, you wont be sorry (unless of course you don't like space games). But if you like Civ2, I'm sure you'll love GC2.