I suspect the difference between an initiate chieftain and a devotee of a god's leadership role would be seen more in how much religion influenced day-to-day decision making, goals and objectives than ih his ability to govern. If you elect a devotee as your leader you are going to see a lot more religious influence in the way the clan is governed day-to-day - after all he is spending 60% of the time leading in the way his god would have done. That might manifest itself in a variety of ways such as a propensity to do more divinations before making important decisions, making more sacrifices and ceremonies before undertakings, supporting more heroquests etc. The seperation of church and state dissappears in a way that a modern western audience probably wouldn't approve.
One real-world example might be Snorri Godi an Icelandic godar who seems to have embodied some of the combination of secular leader and religious leader that the Icelandic position orginally implied. He might be a good role model for a devotee of Dar.
Also don't forget that under the occupation a leader who is a devotee of an Orlanthi cult is going to have a harder time hiding his worship when meeting with Lunar officials etc.
Ian Cooper