A representative from Stardock merely stated, in the abstract, that the better levels of A.I. had access to more « routines » and « sub-routines » in their computational reasoning -- which is extremely vague.
It's not that vague when you think about it, though. The AI is basically a system for gathering all the different variables, happenings, etc and deciding what to do based on them. It should be fairly understandable that progressive AI difficulties would use better methods of deciding what to do.
Let's take for example economy - between Easy/Normal/Hard, they're better at managing the economy.
Another example (not that I know exactly how it works, but for the sake of an example): an Easy AI might see a planet and say "Hey, I'll attack!", a Normal might see the same planet but realize "Hey, my planet's under attack too, I'll go defend it instead", and a Hard might see the same planet and figure "Well, mine's under attack but I got another fleet closer that can beat them off, I can go attack with this one".
I mean, for Ironclad to answer what exactly the differences are could well be a book