Sibylla Bostoniensis

Another factor is the method by which books were copied. (I wrote about this on my blog a few years ago, prepare for info dump).

Europe: one monk makes one copy of one original. After the copy is made, if he wants to check it for errors, he has to compare the two texts by looking between the two copies. All this is done in silence, each monk labouring alone on their own separate book, even if the monastery had a scriptorium where several monks were working at copying books at any one time. Finished books sometimes have endnotes where the copyist talks about how hard and lonely the labour of producing the copy they have just made was.

Islamic world: Islam put a lot of weight on oral traditions and memorization. Written books were just memory aids, you were supposed to be able to speak the full text aloud without looking at the book. This led to a very different method of producing copies:
One person reads the original aloud. As many people as want copies sit in the room with him and transcribe his words. After a section has been transcribed, one of the copyists reads aloud from his new copy, and the person with the original catches any errors (while everyone else follows along on their copy, enabling them to catch errors as well). This doesn't reduce the labour hours required per copy, but it does allow many copies to be made at once, with fewer errors, and it turned book copying into an enjoyable social event.

Source: Jonathan Bloom, "Paper Before Print: The History and Impact of Paper in the Islamic World."

Papyrus disappeared very fast once paper got to the Islamic world (paper making technology arrives in Baghdad around 750, first paper mills open 800 ish). The four thousand year tradition of papyrus making in Egypt ceased utterly within a century of the first paper mill opening there (in 850). Paper tech spread really fast through the Islamic world, getting to Moorish Spain in 1056, and then took an extra 200 years to make the jump to Christian Europe, because Europeans were xenophobic bigots.

(All of the following is also from Bloom).

When we talk about the massive sizes of Islamic libraries compared to Europe's, there are two factors at work - paper vs parchment, and the "one scribe makes one copy" vs "one person reads aloud while a roomful of people each make a copy" production methods.

Al Hakam II, Caliph of Cordova in Spain in the late 900's, was said to have 400,000 books. Saladin is supposed to have sold off a 1.6 *million* book library belonging to his predecessors after he deposed them (1170's). (numbers are probably exaggerated, but even if we knock off two zeros, those are still huge libraries).

And then there were non-royal libraries (where numbers are much less likely to be puffed up). There were multiple libraries called "House of Wisdom," but the one founded in the 990's by Sabur ibn Ardashir had 10,000 books at its height. In the 900's Abu Mansur al-Azhari reported that his predecessor (deep breath) Abu Abd al-Rahman Abdallah ibn Muhammad ibn Hani al-Andalusi, had a private library, which, at his death, was sold for 40,000 dirhams - (books cost 10-100 dirhams depending on how nice they were, that translates to 4,000 books if they were all ordinary, half that if there were 200 nice ones).

Contrast those numbers to much lower ones from China (paper vs paper) and you can see the effect the oral copying method had:

Imperial library of the Tang Dynasty around 721: five to six thousand books. (woodblock printed books were in their infancy at that point, and mostly confined to Buddhist texts). Monastic libraries around the same time had 1-2 thousand books.

In short, imperial Chinese libraries before printing were the size of private libraries in the Islamic world. Imperial Islamic libraries were in another league entirely.

Add in lack of paper, you get even smaller libraries:

Monastic library of St Gall in Switzerland, mid 800's: 400 books. The monastery at Bobbio, Italy: 650 books, and the one at Cluny, France: 570 (both 1100's). Fast forward to the high middle ages, and things weren't much better. The library of the Sorbonne in 1340 (allegedly the largest in Christian Europe) had only 2,040 books, of which 300 were missing (loaned out and not returned). The papal library at Avignon had 2000 books at the end of the 1300's.

Semi-relevant anecdote from from Elizabeth Eisenstein's "The Printing Revolution in Early Modern Europe" (I think, it's been a long time, it may have been a different book for the same class): after paper arrived in Europe but before the printing press, increased demand for books (thanks to the embryonic Renaissance) led to a mass production system where an original copy got divided into dozens of pieces, each chunk being assigned to a different scribe who was to make multiple copies of his section, and then complete copies would be assembled. The resulting frankenbooks were not pretty - they had a different hand every few pages, with some pages crammed with tiny print and others having lots of blank space, depending on how well each scribe was able to make his portion fit neatly on an even number of pages.