I went the opposite route--I played MoO2 for nearly a year before I picked up Civ II. Other then the fact that there isn't any terrain to speak of, they are quite similar.
Similar enough to get you in trouble if you use a civ-style build strategy to play the game.
You will find that colony management is much easier--a six place build queue is a godsend--and that diplomacy is more realistic. You get the impression that unlike the Civ AIs, the MoO AIs are unaware that they're in a game (Allies remain allies, attitudes aren't guaranteed to go downhill simply because you're winning, etc.).
A couple pieces of advice:
Build points carry over to the next project without penalty, so if you want to insert a small projcet ahead of a large project your're already in the middle of, feel free; this is especially true if the small project in question will boost production.
You can freely switch research goals, again without penalty, but research point DO NOT carry over--if you switch to a lower cost goal, you WILL lose any excess points.
Take Automated Factories and Research Labs when they become available, and build them on all colonies ASAP; AFs should be the first thing built on any colony, and when you get them, slip them in ahead of whatever you're building at that moment, no exceptions.
As a corollary (sp?) to the above point, I tend to concentrate on Construction and Computers as much as I dare, reseaching Chemistry, Sociology and Biology when 'comfortable', and Power, Fields, and Physics when absolutely necessary. But that is just me...
Oh yeah, one more thing...building your own races is FUN. I never play with the standard races anymore. Try a creative / lithovore combo. Anything involving cybernetics or subterranean is also good.
[This message has been edited by The Mad Monk (edited May 30, 2000).]