Is there any difference in the AI between the 2 versions, or is the only difference the lack of saves?

I would argue that lack of saves is huge... But to your exact question, other than an increase in armor, damage, etc I dont see any true difference in how "smart" the AI is. His bezerkers will always charge, sorcerer will never vortex, all that good stuff.

Yep, indeed. The manual does indicate an IA improvement on "Hero" (and "Mighty Hero", since it just adds that "Ironman" rule), among other factors (like some reinforcements or additional enemy units on some maps).
Khorne Berzerkers use the "Assault" IA pattern most of the time for example, especially during secondary (semi-random) missions - that behaviour can be altered by modding a certain game file -, but they're also concerned by the "Standing (or Patrolling) Guard" one in the single player scenarios for example. This is easy to check (if only by using the editor) and can be modified at will, including each unit's wide range of charactistics (according a certain level of difficulty), if you're willing to dig in the *.dat files. Now, does the IA make really better decisions in the meanwhile ? It never seemed obvious to me, but small differences in decision-making are often hard to spot in those games...
In the end, even though the game was clearly (and explicitely, as mentioned in the manual) designed for "Veteran" mode, the single player missions still feel completely different (and much more epic !) with the "Hero" (and higher) settings. They really took the time to design missions accordingly in order to provide replayability, instead of just cranking numbers up - as it's often the case in most games.

Now, to answer the question, no, the manual is explicit : "Mighty Hero" only enforces that "no manual saves" policy. That's all there is to it...