Generally speaking, hero units have increased health, ammunition and attack speed. If they're melee units, they usually do more damage per hit than ordinary units, and their attacks are usually non-abortable; if they're missile units, they have greater range, accuracy, and their attacks are more reliable--Dwarven Heroes and Pathfinders don't throw duds, for example.
The only aspect in which a veteran ordinary unit can rival a Hero is attack accuracy--and very occasionally attack speed, although with most units, even 100 kills won't raise them to hero speed. (There seem to be some limits to how much faster you can get through experience alone.) But for most units, a few kills are all they need to max their accuracy.
Remember that there's no standardized definition for a Hero unit. These are, simply, very good fighters of their type, as such, they excel in the areas relevant to their fighting style. A Heron Guard Hero is really tough hand-to-hand, and has enough roots to take an army's worth of damage; a Dwarf Hero is good at making and throwing bottles that don't turn into duds; a Berserk Hero is especially ferocious and attacks with blinding speed so that his enemy can't even react, and so forth.
--SiliconDream
