Playing as the KH:

Only the Hegemon and Kleronomos (sp?) can command large forces as they are the top military leaders in the Koinon.

Cities with governors receive the most funds as they are led by talented and influential men.

Not much else. Any other rules are game-specific. For example, my current Hegemon is royally pissed at a faction for breaking a ceasefire and attacking an ally, so when/if he conquers their capital he's gonna burn it to the ground and kill/enslave everyone.