Additionally, Islam was for a long time wealthier and more populous than Europe - but it was never more advanced technologically.
That's a leftist myth.
Not for long, but it did happen. (Western) Europe in 1000 had very little in the way of technology, having backslid tremendously since the days of Rome. At this time the Muslims were as advanced as any people on the planet. To be fair, they stole a lot of their technology from those they conquered, but they're hardly unique in that.
What almost no Americans realize is that for roughly 150 years (850 to 1000), (Western, Latin) Europe was shrinking. It was being invaded from three directions simultaneously, the Vikings from the North, the Magyars from the East, and the Muslims from the South.
A logical observer might have concluded that this was one civilization that was going down. What happened in reality is just about without parallel in history. A culture on its last legs somehow got the strength to revitalize its defenses and begin an expansion that has lasted till today, although we may be in at the death of that expansion.
By 1100 you would be correct. Western Europe had caught up to Islam in technology, to a considerable extent by borrowing Muslim technology, and has been forging ahead ever since. Meanwhile, Muslim innovation pretty much ceased and hasn't started up again in almost a millenium.
I agree, the Muslim world was not more technologically advanced. Also, it was not the Muslim world alone that saved the classical works. The Byzantine Empire lasted until 1453 and was responsible for extending Orthodox Christianity into Russia and saving much of classical learning.