The point of this whole TLDR is that it is a false dichotomy to compare AI algorithms for chess and for Civ. There is a completely different underpinning play model. It's made more difficult in Civ NOT because of the possible permutations but because of the inability to devise the kinds of databases that chess models use. The Civ AI must play "by the seat of its pants" because there exists no century's worth of opening and ending positions.
The difference is easier to see if you consider the way both chess programs and the Civ program offer levels of play, from most difficult to easiest. The chess program null hypothesis is the scoring of positions, and so its default is to play perfectly. For easier settings, it's simply a matter of selecting the positions with lower scores thus giving the human a chance to take advantage of "mistakes".
Civ, on the other hand, works oppositely. Its null hypothesis is to make the best possible play within the rules at the lowest levels, and then to "cheat" at the highest levels by ignoring rules that bound humans.
I hope this helps to facilitate a better understanding of how the two compare — or rather, how they really don't at all.
This is going to bit OP, but while it needs large opening libraries and complex heuristics to do a chess machine like Deeb Blue (I didn't left these unmentioned because I didn't know about them but because they are somewhat irrelevant for this comparison), it's fairly easy to code a chess program that looks somewhat intelligent and can beat a novice without bonuses. It's not as easy to program such AI to CiV, and the fundamental reason for that is that CiV really is an infinitely more complex game than chess. Yes, possible permutations of chess positions will eventually grow to the point that a computer can't handle, but for CiV it happens much quicker. In chess you can evaluate several positions ahead, but for CiV it's impossible to evaluate even two turns ahead. Even if you restrict CiV AI problem strictly to tactical combat, it's still essentially more complex than chess as in CiV, you can move all you're units during one turn instead of just one, which leads to combinatorial explosion much quicker. Chess really isn't a particularly complex game in computing/mathematical perspective, and that's the fundamental reason why chess computers do so well against humans. In slightly more complex Go computers suck while there are lots of research put there too.