Well, the AI doesn't really have any cheats. At least, it's not supposed to. I mean, if we find one then I have to correct it.
I'll let the players answer your question in terms of their experience. But I'll try to give some of the most important differences.
When things go badly the Roman Senate will interfere in the Roman elections to get leaders with higher rankings. This effect increases with each level of difficulty. Basically, the criteria are made easier. This is also true for the criteria used to decide when/if to expand the number of Roman leaders to 5.
From the Introductory level to the Normal level the AI makes better decisions for using its naval forces. At the Introductory level the AI is intentionally stupid. It will occasionally make a good move, but it isn't smart about concentrating its squadrons into fleets that are hard to attack. As a result, you can peck away at it if you want to - much of the time.
The Normal level does a better job of concentrating its naval forces, and is more aggressive about "raiding" to attack your forces when it has a large enough fleet.
At the Hard level of difficulty the AI is a little more aggressive in naval engagements, and makes a few decisions a little better than at the Normal level.
Because the game introduces the ability to decline Pitched Battles, and to abandon sieges under certain circumstances, the decision making for the Normal level has many differences as compared to the Introductory level when it comes to directing armies. There aren't so many differences between the Normal and the Hard level in how land forces are handled. But the Hard level does a better job of assigning Roman leaders to move for the purpose of recruiting.
Also, the AI at the Normal and Hard level is designed to be streamlined. There are fewer cases when a leader is assigned a command phase and doesn't do anything, or merely moves into the field and then back again into a city.
The differences between the Normal and the Hard levels are really something that player should learn by playing. At least, that was my intention.
I hope that this helps.
Forced March Games, LLC