The main reason a lot of classical learning fell into disuse in the West was that the Germanic peoples migrating in didn’t care much, and there was a language barrier - most stuff was in Greek, and they only knew Latin, for the most part. With a very few exceptions, nobody was going around actively destroying stuff. Indeed, the Church is the main reason so much was preserved in the West, particularly some later popes that took a keen interest in the preservation of ancient texts. Easily the worst thing the West did was the burning of Constantinople during the Fourth Crusade, because again, the Byzantine Empire, even what remained of it by then, was a real center of learning and probably easily the biggest surviving repository of books on the planet at the time, so undoubtedly we lost some texts then.
This isn’t really a religion vs religion thing - the Christians came into an existence in a society and region already steeped in Greek learning, and slowly assumed political control over the region. The Muslims were in an entirely different situation: they were from an underdeveloped region and came into the Middle East via conquest. They simply didn’t know what they had, and the violence of the conquests was a major setback. In some ways, the region never really recovered - that and the Mongol invasions.
