Sadly, I don't like the reasearch methods much in either GC2 or Civ 4. That whole "Okay guys, we just discovered X. Let's PICK what we want to discover next" seems a bit forced to me. Unnatural, even. I really liked that blind reasearch thing Alpha Centauri had, where you sort of picked a reasearch area, but discoveries would be made as they happened. Or something like in the first Master of Orion, Theme Park, and Europa Universalis 3, where you have six or so areas an allocate funding seperately. Space Empires 3-5 also had that neat thing where they divided theoretical and practical research up although I don't think it was particularly implemented well.
I like how both games lack tactical combat. I *like* tactical combat, but it feels really inappropriate in an empire builder to me. I mean, in a 4x game, you're, what, the president or king or something. Not a general. That and these sorts of games lend themselves to having very big armies which are already fairly unmanageable, so throw in a seperate battle system...
Anyway, throwing out some quick advantages Galciv 2 has. Not inclusive. Just some stuff I liked.
First, you get capships which can explore anomolies, effectively levelling them up. They're sort of like a hero unit in the HoMM games, and also give the game a bit of Star Control 2-ish flavor.
Second, Galciv 2 has really cool diplomacy. The races are pretty unique, there's this parliament thing which is quite cool, and the AI is very nice.
Third, the technology, I think, is a bit better. A lot of it has a direct statistical effect on your society, which makes it feel a lot more relevant.
Fourth, starbases

Stuff Civ 4 did better I, I thought:
Resources. Trade is really well done in Galciv 2, sure, but in Civ 4 it's just more detailed. You can't build axemen without bronze, or nukes without uranium. Anacreon, a 4x in space, had something like this -- food as resources, along with something called ambrosia which was a bit of a drug, money, and some construction/fuel things. I believe Fragile Allegiance also had a more detailed resource system, although I think you were mostly selling those. I think something where you had certain resources you'd need in GC2 would be neat. It was sort of approaching that with the little happiness/cultural/whatever resources on the map, but couldn't they be made a bit less abstract?
The tech tree itself. GC2's was bigger, but researching the wheel is a bit more epic than researching "lasers 3" or whatever.
I like the notion of terrain that Civ 4 has that you don't really get in space. Terrain modifies in combat, moving... needing to research boats to get across the ocean. Stuff like that.
Civ IV just seems a lot more balanced at times, honestly. I can't really explain this one, but from a numerical standpoint, some things in IV seem sturdier.