I'm not sure "growing secularization" is a proper description of 13th century Europe, except as compared to Islam. The sole unifying factor in Western Europe was the Roman Catholic Church; yet the Church, led by Popes, often conflicted with secular rulers, notably the Holy Roman Emperors. The dispute often centered over issues such as the Emperor's authority to tax church property and name bishops and archbishops. Arguments from both sides ranged from philosophical discourse to personal insults. Both relied on different interpretations of Pope Leo III's crowning of Charlemagne as "Emperor of the Romans" in 800--did he "crown" him as Emperor; or did he rather acknowledge the fact that Charlemagne was already Emperor in his own right? The most serious dispute was the Investiture Controversy between Pope Gregory VIII and Emperor Henry IV. A good source to explore this is Brian Tierney: The Crisis of Church and State.
No such dispute existed in Islam. Under the Abbasid dynasty, a virtual theocracy existed. Officials known as ulama ("those with religious knowledge") and quadis ("judges")settled disputes and set moral standards. They were not priests, but had a formal education that emphasized the study of the Quran and the sharia. The ulama were pious Islamic scholars who attempted to develop public policy in accordance with Islamic law and custom. The quadis heard legal cases and rendered opinions. The Abbasid Caliphs also maintained a standing army and established ministries of taxation, coinage and a postal service.