Here's how I rank the AI traits:
Agricultural - More population, more shields, more commerce, faster expansion, faster research, etc.
Commercial - The commerce bonuses and decreased corruption really help. A runaway commercial AI can out-research me at 50% when I am at 100%. They always have GPT lying around while they are out-researching me. (I try to keep all AI, especially commercial ones, from Sanitation)
Industrious - Industrious AI actually improve their land. They will have their whole territory railroaded while other AI are clearing jungles. The shield bonus gives them a few more units and buildings.
Scientific - It's hard to stay ahead of the AI when they are getting free techs. The cheap buildings make them tougher, sooner. They love using SGLs when I'm almost done with a wonder.
Seafaring - The biggest bonus seems to be the extra commerce which helps their research early in the game. They make contact with distant civs sooner. Also, they love colonizing islands that have a resource I need. The Dromon and SM are no fun to fight.
Religious - Their biggest advantage is culture. They will build temples early and often, and a religious civ on my borders during the MA is no fun when they start cranking out cathedrals. Beware the culture flips. The reduced anarchy doesn't matter much because on some difficulty levels the AI never spends much time in anarchy anyway.
Militaristic - The militaristic bonuses do not compensate for the AI's lack of war-making proficiency. You can't fix stupid.
Expansionist - The AI starts the game with knowledge of the map and resources. When the AI starts with a bunch of free units, they are essentially expansionist anyway. The goody huts help them for a while, I guess.
As far as map size goes, smaller maps encourage aggressive play, so beware a civ with an AA UU.
More water favors seafaring and hinders expansionist.
I think that these rankings are consistent between difficulty levels.
I would rank these traits a little differently for a human player. Seafaring is #1 on archipelago maps, and a human player can actually take advantage of the militaristic trait (see: armies). Also, scientific may be more valuable to a human than industrious because the human can build a ton of workers. Just a note about the AI's free units: They don't build currughs, but if they start on the coast with Alphabet, sometimes they will get currughs as free units. Try keeping up with that.