The fanatical Christians that burned books were led by Girolamo Savonarola, 1452-1498 who later became Pope.
Whatever survived until 620 AD was destroyed by the Muslims because it either contradicted the koran, or was already mentioned in it. What was preserved by a few muslims were works that interested them. All else they destroyed.
The muslims are single handily responsible for the destruction of Classical Western Civilization, Classical Christianity and the majority of written works that survived until the 620-661 AD period.
The Roman Diocletian 284 - 305 AD book burning was long preceded by burning of the Library of Alexandria of which various people are blamed from Julius Caesar in 48 BC to Mark Antony to Theophilus to the muslims in 640 AD.