I've played 4 or 5 games of LH so far, and, while I think Stardock has done an incredible job making the game more enjoyable in terms of game mechanics, visuals, tactical battles, and (particularly) heroes, the strategic AI still needs a lot of work. In all of my games, I far outstripped the AI. First on challenging, then hard, then expert, and then even insane. As in, I'd meet the AI and I'd have 60-70 power while they'd be at 20-30. It's not me - I'm not that good.
To better provide feedback to the devs, I started 2 new games with cheats enabled. I turned off fog of war, here's what the AI was (or wasn't) doing.
Game Settings
Hard / Hard
Normal monsters
Medium World
Dense resources, magic
3 AIs
First game had some of parrotmath's mods active, but I turned them off for the second game.
Edit: version 1.1
Overall Observations
None of the AIs started building anything until turn 10. Ignoring their poor first building choices for now, why would they wait until turn 10? Can someone else try to repeat this? Ctrl-U is the remove fog cheat once you enable them.
The AI is not intelligent about city enchantments. It seems almost like they can only cast one per turn, and cannot cast them on the turn a city is created. Mana isn't the issue, as often they wait to cast Meditation (0 mana cost). They seem to prioritize enchantments on their sovereign. Is that deliberate?
This has been an issue I've reported since the FE beta - the AI often loses a turn of a city or an outpost because, once a settler arrives, they need to wait until the next turn to settle or build the outpost. There's no reason for that.
AI sovereigns and champions like to sleep late and sit on the couch eating cheetos, or something. I didn't count, but for half or a third of the first 10 turns, the AI sovereign just sat there doing nothing. Nothing. It's like they can't cast an enchantment without losing all of their move.
When they did move, they'd often spend all of their move going one space on plains. As if grabbing a goodie hut or quest ended their move for the turn even when they should have one or two move left.
Another that I've reported since FE beta - AI units departing cities move one square out of the city and no further. It wastes and entire turn of that unit's movement.
Intelligently setting taxes - all of the AIs left taxes on low. They got 0.8g in return for 12% unrest. I can't imagine many players make that same trade, but people who are better than I should weigh in.
That's the main list, here's the turn by turn.
Game 1
I found my city, turn taxes to oppressive, garrison my sovereign, and watch the AIs.
Turn 1
Magnar: Started on a 5/3/1, there's a 2/4/3 nearby that might be better
Carrodus: Started on a 3/3/0, he's next to a 4/3/0 that's a little better
Kulan: Started on a 4/3/2, that's the best around
Turn 2
Magnar: He did nothing - just sat there. Didn't found a city. I think he cast burning blade on himself and called that a turn.
Carrodus: Founds a city on the 3/3/0, which becomes a 3/3/3. I'm ok with the AI cheating, especially on Hard when it has a crappy start.
Kulan: He did nothing - just sat there. As with Magnar, I think he cast some self-enchantments.
Turn 3
Magnar: He moved to the 2/4/3, did not settle. Ended his turn there
Carrodus: He's moving around to grab some goodies, or maybe to attack some wildings. Could go either way.
Kulan: He settles the 4/3/2
Side note - all the factions founding cities stick with low taxes, increasing unrest by 12% in exchange for something like 0.8g. I don't know what other people think, but a 12% penalty to research and construction seems not worth it for 0.8g.
Turn 4
Magnar: Finally settled the 2/4/3, but didn't go anywhere afterwards
Carrodus: He moved one space, not 3 towards a goodie hut
Kulan: He sat in the same place, didn't move
Side note - on season 4, not one of them is actually building anything
Enchantments:
Magnar: He just founded the city this turn, so maybe he gets a pass, but it has 0 enchantments (3 essence). Oppression is possible
Carrodus: His 3 essence city has meditation. A good choice, but he has life and air - propaganda and sovereign's call would be amazing on that city. Carrodus himself has 2 enchantments, so maybe he used mana on that. Neither is tutelage though.
Kulan: His 2 essence city has meditation also, but is missing oppression or propaganda. He was smart enough to cast tutelage on himself at least, Maybe that's where his mana went.
Turn 5
Magnar: He retreated to his capitol at full hp, which now has meditation
Carrodus: He grabbed a goodie hut, continued enchanting himself. He now has Evade, Courage, and Regen. He somehow used all 3 of his move moving the one space to the goodie hut.
Kulan:
Still no one constructing anything.
Turn 6
Magnar: He left the city solo, but stayed just next to the city, didn't actually go anywhere
Carrodus: Stood still
Kulan: Stood still
No construction from anyone yet
Turn 7
Magnar: Moved one square into the woods. Now has oppression!
Carrodus: Killed some wildings and leveled to 2
Kulan: Used 2 move to move 1 space on plains and got a 2nd goodie hut. Now has oppression!
Turn 8
Magnar: Moving solo through the woods
Carrodus: Used 3 move to capture the goodie hut of the wilding it killed last turn
Kulan: Heading towards a weak quest
Why isn't anyone building anything?
Turn 9
Magnar: Just got out of the woods
Carrodus: Retreated to his capitol to let a hurt militia recover
Kulan: Successfully quested, got a second hero
No one is building still
Turn 10
Magnar: Quested, got a second hero. Just started a monument
Carrodus: Carrodus left the city solo. Used all of his move moving only one space out of the city. Started building a bazaar.
Kulan: Stood still, champion stood still. Started building a merchant
Turn 11
Magnar: Magnar's headed back to his capitol, second hero stood still
Carrodus: joined outside of the city by one unit, but didn't go anywhere
Kulan: Joined into an army with his champion, got a goodie hut
I was kind of amazed by this, so I disabled mods and started a second game. Same settings.
Game 2
Turn 1
Magnar: On a 4/3/2, that's the best around
Relias: On a 4/3/2, that's the best around
Verga: On a 4/3/2, that's the best around
Turn 2
They all settled their 4/3/2's, but no enchantments, no construction
Turn 3
None of them move, no construction, some enchantments. Magnar and Relias went for Meditation, Verga for Enchanted Hammers. Why didn't Verga cast meditation also?
Turn 4
They move and cast their second enchantment. Why not last turn? Still no construction
Turn 5
2 of 3 moved, still no construction
Turn 6
2 of 3 moved, still no construction. Magnar is just sitting there 2 spaces from a couple skeletons he could easily destroy.
Here's the sequence - I screenshotted 6-8, but he's been standing there since he moved there on 4:
Turn 6:

Turn 7:

Turn 8:
Turn 8:
Verga didn't move this turn. Magnar finally moved into the woods.
Turn 10:
They all start building