As a non Muslim,I do not understand the difference in preferred government style between the two branches of the Muslim religion. I understand the lines are very blurred in the Muslim world. There still seems to be a clear distinction in the preference of government style of each branch. One seems to prefer an authoritarian republic with a partial democracy. While the other prefers an authoritarian regime. I also perceive huge inconsistency among even the most orthodox Muslim scholars. From my understanding there is no mandatory requirement for each branch.
I feel that this question needs to be asked. It seems to be a global issue that has caused much conflict. I think a better understanding of this topic would help Non-Muslim world when confronted with global issues.