OK John Hughes ... I will say that a Sovereigns EGO will require his pompous and illiterate Ass to manage the city, even if he has a better Champion. I suppose the only case that should NOT happen is if your sovereign picked non of the negative mental traits (cruel, blunt, insane, murderous, arrogant) AND your race has egalitarian.
In Rome Total war, a governor's Management skill determined the governor ... even if someone with a lower management skill had more popularity (better citizen morale), more law skills (reduced maintenance) and better tax skills (more gold). Still, the management skill did affect many of those things in base-output, so usually the person with higher management skill was better.
Now, if two people had the same management skill, it was the elder sibling that had dibs, NOT the person with better skills. I think that elemental will probably have Prestige/Fame/Political Power being the determining factor. Usually this will equal the overall combat rating of a unit ... however it could also heavily be effected with the amount of questing (their name has reached legendary renown, gaining much personal prestige). In this case, yes your average Joe Champion could potentially gain greater personal prestige than the Sovereign, however the Sovereign would start out with an inordinately large amount of personal prestige (probably 50 or more).
(personal prestige is a static number, that is increased by level, combat ability, and quests/achievements)
Two things could happen if an underling's personal prestige increases MORE than your Sovereigns. If their loyalty is low, they would create a revolt/civil war. If you are Arrogant and Cruel you will have them assasinated (automatically) and if the assasination fails then their followers will turn against you (civil war). If however, you are a nice sovereign, and their loyalty is high, the probability for Civil War will be very low.
essentially, you DON'T want an Underling to become more popular than you, but if they do, then they can become governor of a settlement.