I've played both, and I actually consider Galactic Civ to be a spiritual successor to the Master of Orion games. GC2 has some nice features that the MoOs don't have, such as the ability to zoom in and out of the tech tree, and a very detailed story (I admit, I don't know the half of it, since I've only been playing on and off for six months).
I also don't believe MoO 2 limits the number of slots on a planet for improvements (so it can get quite crowded on those tiny words), so long as your economy can support it. As for MoO, it didn't have any planetary improvements at all, just sliders for research, production, and defense. That's it. GC2 also seems to borrow from Civ3/4's idea of cultural boundaries (although, in MoO 2, you would irritate some aliens if you built/had a planet in 'their' star system (even though you may have been there first). Heaven help you if they colonize the planet next to your homeworld.
I think the latest GC2 had an Alteran analogue (bad guy aliens that come in and destroy your fleet/bomb your planets), but my memory is fuzzy. GC2 does support major and minor races. Spying was severely nerfed in GC2. You could rob a civ blind in MoO 2 with a certain sneaky non-human race. Also in MoO 1/2 conquering a planet from a more advanced civ (sometimes a difficult feat, especially vs those bears) usually netted you 1-2 tech improvements.
I think there were some differences when it came to natives and alien race integration (not sure GC2 did this; I think they just give you an economic penalty when you capture a planet).
All in all it's a good pair of classic games, and in my humble opinion, it's worth it. Yeah, the graphics aren't all that great, but if you want to see the parent of GalCiv and GalCiv2, give it a go.