Obviously, this is a combination of good UU/UA/UB, selection of policies, and leader general style when handled by the AI. To give an example, I have yet to see China or Arabia getting really strong, although they are arguably among the best civs to play, while I consistently see Germany getting strong, or even more Siam and Byzantines.
China, Arabia, and Mongolia are very strong in the hands of the player due to their ranged UU. Unfortunately, the AI does not have a full mastering of ranged combat, so it's not going to do as well with them.
The AI is pretty sucky at diplomacy (with the player and with each other), so it's not going to benefit as much from the trading opportunities that Arabia and the Netherlands have.
The AI also does not have a good handle on religion, often taking terrible combinations of beliefs. AI Theodora might do okay with the two early UU's, but I have NEVER seen the AI use her UA well. Heck, I have NEVER seen the AI choose a sufficiently respectable religion that I (a human player) would consider!
It seems logical that the AI is going to do best with "easy to pilot" civilizations which doesn't require much thinking. Greece, Germany, France, and the Iroquois are all pretty straightforward. Also Persia. On Deity level games, I tend to find Persia to be the biggest problem due to the insane happiness bonuses that the AI gets (easy for them to get Golden Ages) and how overpowered Pikemen are in G&K. Persia builds lots of Immortals (who keep double healing when promoted) and prioritizes Civil Service (providing both Pikemen *and* Chichen Itza) so Persia is easy to play and plays to the AI advantages.
yeah he does. he chops like mad too so his starting bias are of double value. He's a very likely runaway. Actually, I believe only two factors count when you think about how well the AI will do. Does it spam cities? and Does it conquer city-states? I'm sure 80% runaways are yes-no.
From my experience, the significant majority of runaways go the Liberty route. Tradition is a very distant second. And Honor isn't even in the race. Honor civs usually build a massive early army. Occasionally they manage to take some cities early on but most of the time, they sit there with their giant army and one city until they are out teched by the Liberty and Tradition civs.
On a similar note, civs that I see the AI does extremely poorly include Denmark and especially the Aztecs. Montezuma is so over the top aggressive that he spends most of the early game building Jaguars but ends up picking too many fights and dying. Denmark tends to do pretty poorly as well but probably because the AI can't understand how to use Denmark's awesome UA well. Being able to move/attack after disembarking (and keeping your extra movement points) is insanely good. Free pillage was okay when the game first came out, but is now very strong since they changed pillaging to provide limited healing. So Denmark should be pillaging everything in sight, which it does not do.
Just a side remark on the criteria AI uses to declare war. As is well known, the most important is the military power - this is normal and seems obvious, but it is incorrect both in civ and in reality. Current military is one serious parameter, but technology AND money are a second, more important parameter.
According to the code, money is a factor (but not as major as current military strength).
But in practice, I have often baited a civ into attacking me by maintaining an obsolete army, which I upgrade as soon as he starts the war!
(eg. 67 techs to 47 me/AI), conquered aggresively 
, built Apollo, had 100+ City defenses 
, Thus in both games I was fighting him with Worldwar Infantry or even Riflemen, Cavalry, Frigates and Artillery, whereas his army had Modern Infantry, tanks, planes, Battle Ships and rocket artillery. Not to forget that he DID have more soldiers on demographic screen. I won both wars though, because he was too stupid to throw everything he got at me (and that's a showcase example of how bad AI leads military). Geez, in one game HE HAD A PLUCKING CONTINENT for himself! And I conquered hist coastal town because I've cleaned a sea corridor from me to him with five frigates, beating two battleships on the way, while his other five or so battleships just watched!
whatever)...He is boxed up in a mountain and hills as if he was Incas and its the first time I see the AI use his units in a rotation pattern (remove the first rank to heal replace with fresh troops, rotate again). And to top it all he has the Kremlin....If bombers dont get him I dunno what will.
