This is a rather broad question, and I would point mainly towards the religious aspects of the caliphate as a system of government - it might be helpful if you clarify what period of Islamic rule you are talking about, though. For example, the Ottoman Caliphate is very different from the early empire created during the 7th and 8th century Muslim conquests. Relations between the central government and provincial management are another area you could look at, or perhaps how rulers claimed authority. Bureaucracy, too, would be an interesting area to contrast the types of government.

Also, due to the way you phrased the question, I’m going to include the subreddit homework policy as a reminder below:

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