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Recruit and Warrior: essentially, the only difference is in the amount of starting gold and the rate of neutral creature spawns. The AI doesn't use spells above level 3 and isn't overly aggressive against you.
Veteran: the starting amount of gold and resources is the same for you and the AI players, and it's not 50K or 30K, but 20K. The AI uses the entire range of available spells of any level and is extremely aggressive, especially against a human opponent. For example, I played on Veteran with Necromancers on a huge, randomly generated map, and it felt like a group of allies were simply playing against me.
On Hero: you have 10K gold (the AI now has 50K instead), and you have almost no resources, so play however you want.