Basileus = Highest level player of the entire faction. (If same level, then highest prestige)
Basileus decides what players become Ephor, Elders, Noble (the number of spot depends on Faction Power)
Basileus can mark players as spy (spy do not affect FOR in any way, but count as a player for launching Area Battles)
Hierarchy affects the following:
Faction Occupation Rate
The higher your hierarchy, the higher FOR you gain by winning a battle, the higher FOR you lose by losing a battle. (Basileus in military center winning another purple Basileus can get up to 9-12% FOR)
FOR gain from investing is decreased (by ~50% I think)
Prestige
Being the first to attack Nobility in the Wanted list will give you 2000, 3000, 4000, 6000 o prestige for Noble, Elders, Ephor and Basileus. (Wanted List reset each day)
Faction Power
Any player winning a battle over Nobility will increase their Faction Power, which gives more nobility spots that Basileus can assign player to. (Most faction assign least spot possible to avoid losing FOR) (Faction Power reset every 4 game years I think)
Attack/Defense bonus
Basileus: 5%
Ephor: 4%
Elders: 3%
Noble: 2%