The pikes versus tanks thing is fixed, but there are some things that can make it more likely to happen. One major thing is that damaged units don't attack at full strength, IE half hp=half strength. So if you find a low tech enemy and continually throw units at him ignoring damage and expecting to win constantly don't be suprised when your exhausted units get taken out.
As for the others, did you guys play Civ3 that much? Empires fell and rose all the time. It wasn't uncommon in Civ3 to see the biggest empire ganged up on in the middle/industrial ages creating a new balance of power. One killer AI usually pops up per continent, and its definitly not always just who was strong early on. I've also had games where all the empires were close in strength(which I loved, because those make for some tense situations).
I've even watched an AI go from less cities then the surrounding civs to conquer one...then conquer another..and so on until he took down the other five civs on that continent and was a superpower I couldn't hope to match. As for HoI(1-2) and Victoria being more complex thats up for debate, Civ just presents its information better so you don't have to go hunting for it.
Another word on combat in Civ4, theres sort of a paper-rock-scissors system going on that requires combined arms. For example Catapults are good against Melee(and can damage all units in a stack, making SoD a thing of the past) but Horse Archers are good gainst Catapults and spearmen are of course good against Horses. Its defined as Artilley/Melee/Horses obviously. Also Archers(finally) are the standard defensive unit until guns, they get bonuses when defending cities.
If you want a look at the techs and promotions, check this download of the tech-tree and promotion list. http://www.2kgames.com/civ4/downloads/civ4-techtree.zip
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