Were postclassical european kingdoms mostly similar or most different from islamic caliphates

You could argue that they were very similar because of the connection between religion and state. The states had leaders but the leaders all ultimately answered to religious leaders even though they were kingdoms on their own. The difference was that the Islamic Caliphates had leaders that were also the leaders of the religious world, while the leaders in European Kingdoms answered to people like the Pope who was a religious leader regardless of the kingdom.

What war are you specifically talking about?