I'll give you some positive aspects and some negative aspects.
Positive
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* You get to play intelligent (most of the time
) competitors.
* You get to engage in real diplomacy/bartering. No strict restrictions in foreign relations like you have with the computer.
* Face new challenges and increase your civ skill and knowledge.
* Make "civ friends" (That sounds queer, but you know what I mean hopefully
* The most important aspect is that you get to test your skills against real people I think.
Negatives
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* Some times hard to find a good game. Easy to pick up a game, but hard to find a game that keeps your interest. This is usually determined by the quality of the group you play with.
* Connection problems. Ineveidable. If you lose your internet connection even for a second while in a game, you get booted and have to re-enter. This is more of a headache than it sounds.
* People don't show up like they say they will. This happens a lot unless you take some time to plan a game.
I personally have not played a single player game since I got civ gold in October. In my opinion, why would you want to play the predictably simple AI when you can play a real person?