Flavor
Religious
Culture
Science
Gold
all good techers, for the most part. "Flavor" weights the techs the AI picks beyond the normal weighting the tech has (i.e. Feudalism is high for all), and AIs are capable of thinking ahead at least a couple techs especially when it comes to sniping 1st-to-research rewards...in debug/cheat mode you can literally see them picking Economics as their goal and auto-teching the prereqs like Edu + Banking.
Early on in the tree, Religion/Culture/Science are mostly intertwined so any of these AIs can tech quite surprisingly well. Gold pushes them similarly as both Science/Gold (Education > Economics) and Gold/Military (Guilds >Banking) intertwine. Ever see Mansa or Huayna with fast rifles despite never being at war?
Religious/Culture both have cultural overlap. Either can push for wonders or religions.
Military
rather intuitive, they collect military tech with high priority and are usually your common warmongers. Shaka will race to Engineering, Cannons are more likely early out of them, etc. These guys LOVE Grenadiers.
Production
Growth
Less clear what effect these flavors have, if any. I know BW and RP are definitely Production techs, so it has some tie in with war. HC notably is a Gold/Production flavor leader and can be rapidly powerful militarily if he gets land.
Peace Weight
Readily apparent to anybody familiar with the game, it drives war behavior and general AI attitudes that promote factionalization. Peaceful civs make buddies and tech, warmonger civs attack and either get huge or stagnate.
The civs that perform the best regularly tend to be the ones with good teching flavors but are still warfaring enough to attack someone they don't like -- your Justins and your Zaras, instead of your Gandhis and Rameses. Simply militant civs can always run away if they get lucky and snag huge land but it's hit or miss, not reliable, and they won't necessarily be good in the tech race until their land advantage kicks in.
Peace weight is but one factor and can be superseded by many things (religion being the most common), but acts as the general tone-setter between relations. It's the reason Hatty and Augustus may never attack each other if even founding opposite religions, the reason Gandhi is picked on, the reason Stalin and Shaka are bros despite being in opposite religions and attacking each other's buddies, etc.
Attitude Thresholds
Specifically whether an AI will DoW at a certain level or not. AIs with lower thresholds are less restricted in their own behavior, and are more susceptible to being bribed. They'll fight with someone more often just because they don't like them and will jump into all kinds of wars.
Generally works out better for the AI if they can attack on their own at Pleased and are hard to bribe, as they mostly choose when they want to war; this can make certain low Peace Weight guys particularly dangerous (think Giggles, who WILL attack people but require Friendly for bribes; Caesar/Stalin can be similar requiring Pleased for bribes but being fairly aggressive) Being unable to DoW until at least Cautions can lock them out of crushing a weakling, while accepting bribes easily means they can constantly be caught in disruptive warfare.
Peace Weight and especially religion usually push AIs into camps where their thresholds will either hold them back or allow them to improve their position. A great example of this is the resident best AI, Justinian : can't declare at Pleased...but he's middling in Peace Weight, and a religious zealot....Justin will easily find targets he doesn't like enough to attack and not have his hands tied to sit in a corner.
Other Factors
-Anything that lets an AI expand quicker or secure more land with borders is a huge boon to the AI. Land is power, especially to the AI who grows like a fiend and works all the land! IMP and CRE are large advantages to the AIs for pumping settlers faster and claiming land with culture; Most (all?) CRE leaders tend to also be a fast teching Flavor too! Land-grabbing potential is one of the strongest advantages an AI can have, and is how you can get otherwise not impressive-on-the-surface leaders like Cyrus and Kublai who are actually fairly strong AI players!
-Other traits can have some impact. Mostly FIN as the AI is fond of cottages and with their whip-light playstyle, working as many tiles as possible, it offers a huge amount of bonus yield. Any FIN civ has the potential to be rather amazing especially if they get large, even Ragnar or Wang, though their other attitudes usually sabotage their game otherwise. Liz and her rampant culture focus to the detriment of her military combined with her very high peace weight are a good example.
-As the article points out, rating the AIs on anything requires a composite look at what they do and how they play out. When they have a combination of favorable things they do better with more consistency. Having a major caveat (like Toku's infamous border alienation or Gandhi's super peaceful nature) tends to overshadow what other strengths they have.
-Certain strong civs may not seem to follow the land grabbing part, but nonetheless their combination of flavors + peace weight + thresholds and serious advantage in an area make them powerful nonetheless. Mansa is the undisputed best techer in the game, Pacal is the best cultural civ, etc. and they have favorable thresholds + flavors -- Pacal is even "Low" in peace weight so true Warmongers are more likely to leave him alone and he's more likely to attack other squishy peaceniks. They are also consistently powerful contenders if able to grow, and even if not, will still contest in their respective areas of strength!
So while inferences can be made based on data, I've learned more from actually watching the AIs in game and noting their successes and failures. There's no doubting that some of the most consistently strong AIs -- Justin, Zara, Mansa, HC, Pacal -- can be explained by the information, but that doesn't mean that other AIs that CAN do well like Cyrus, Hannibal, Cathy, JC, Ragnar -- aren't potentially major threats, as I have seen in-game.
If you're interested in seeing it in action or hearing more of the reasoning and stuff behind it, check out Sullla's AI tourney stuff:
http://www.sullla.com/civ4survivorindex.html
It's a lot to read but offers a bit more of the observation side vs. pulling numbers, and you get to see it apply. Obviously the sample sizes are nowhere near large enough to be definitive and there are quite a few flukes, but it's a neat application in practice to see it.