First of all I'm not a fanboy.. I played Civ competitively a lot during Civ 3, and some early on in Civ 4, but Civ 4 lost my interest and I didn't end up getting all the expansions. For the most part I like Europa Universalis variants a lot better because the multiplayer is less exploit oriented. For the Glory for instance is really well done, and plays well. I also really don't mind being restricted to one world map with the AI designed specificially for it, as opposed to throwing in any type of map under the sun even if the AI doesn't understand how to play on it (Archipelago players know what I'm talking about!)
My biggest frustrations with civ is the way combat works. I hate the time scale that wars play out on. Multi-turn battles in this game in the ancient era mean fighting over 100's of years. I also hate the fact that units don't have a supply range. A unit that is 100 years of movement away from your territory should never reasonably be considered part of your civilization (part of this is time-scale again). Also I think way too much effort is put into making the map look really "pretty" at the expense of being able to run quickly in multiplayer or being able to support larger size maps more easily. For once in Civ I'd like to see a playable world map.. and by playable I mean a Europe that could actually support say a capital and a 2nd city for the 10 or civs that most people would base there. With many of those civs not available in this game I'd like to be able to see France be able to have most of its major cities actually fit on the map, along with the same for Germany, England, Rome and Greece. I'm not talking about having to fit say 30 cities for each of them, but it doesn't feel like Europe if these civs only have 2-3 cities each. It also feels a little silly that it sometimes takes several hundred years to build a single city improvement. Also a lot of the guessing about future techs feels quite lame. I would prefer a game that replaced the Alpha Centauri space ship victory with a tech victory by say being the first civ to land on the moon. The slightly compressed time scale might also allow for a bit more depth in the eras of the game before the outcome is already decided.
While Soren has gone on extensively about the problems with Total War (complex interface, then once you learn it you can crush the AI too easily) Civ has much of the same problems. First of all the interface is buggy, and a lot of the click options lag or freeze up forcing you to click off to get them to respond. Secondly, the AI in Civ is only competitive at levels where it cheats heavily, and the player has no control over how the AI cheats. In games like Total War, there are ways to control what advantages the AI gets, so for instance if you want to play a challenging build oriented game, you can give the AI bonuses in combat so that you have to outbuild them and beat them with better units. In Civ, you are almost reduced* to playing a strategy involving some sort of early game attack at Deity because you will not catch up to the opponents start without it. My usual solution to this problem was to find strategies that didn't work at deity but were particularly good in multiplayer and in Civ3 I was on top of one of the Case's ladder (which was good back then) for some time doing this, but I insisted on turn-based play, which just isn't an option anymore. Click-racing is a huge problem that ruins multiplayer for me and many others, especially when all the bells and whistles they've put into the game lag it substantially, and even more so when your pre-moves are executed at end of turn instead of at start of turn! I really think Civ needs a real-time mode that basically fixes the economic times, and does unit movement in pieces so that you can't move entirely at the end of one turn then entirely at the start of another. Most games have gone to something like this for MP as it works better than turn-based (issues with length of game) or simultaneous turns (issues with exploits).
* most of the other tricks to beating the AI involve abusing the decision making in the diplomacy window. For instance, the AI is far too likely to accept loan deals, even as you gather units on their border.
