I remember reading about the mongols sacking Baghdad, from which it has not yet recovered, and am wondering who really did the most damage to the region. Was it the crusades or did other factors contribute more strongly?
pretty much certainly constant invasion by steppe peoples. The steppe nomads were really, really brutal in their how they conquered people, during the invasion of Khwarezmia they erased entire cities from the map, the majority of the Khwarezmid army of 400,000 men was killed outright (a high figure even by modern standards, the Syrian civil war killed 76,000 last year) and the entire population of Samarkand was killed. I don't have figures but Samarkand was one of the great cities of the time with a large population. The Mongols also sacked Urgench, with an estimated 1.2 million civilians killed. . It is estimated that Tamerlane's conquests, which took place mostly in Persia, killed 5% of the world population at the time. The total population of Persia may have dropped from 2,500,000 to 250,000 as a result of mass extermination and famine. Bear in mind that Persia at the time was a centre of Islamic culture and learning with some of the best scholars, jurists and engineers ever. Their poetry and cuisine was famous across the Islamic world and it was poorer as a result of the steppe invasions. The Crusades were small potatoes by comparison. The upper estimate of people who went on the First Crusade is 80,000 and the invasion was relatively bloodless by comparison.
What was the worst thing to happen to Europe in the last 100 years? WWI, the Holocaust, all the Allied bombing attacks, Operation Barbarossa, everything that happened east of the Iron Curtain... There was a lot of bad stuff. And that's just in 100 years.
The period you're asking about lasted almost ten times that long! Without a reliable measurement for damage, it's almost impossible to say with certainty what was the most damaging event in the Middle East during this time. Lots of bad stuff happened, and comparing them is hard and subjective. For example, a Muslim might consider the spread of Islam to be the best possible scenario, but a Syrian Christian ~700 AD might have a different response. The Turks adored the spread of their empires. The Byzantines, not so much. Even the sacking of Baghdad isn't so bad from a Mongolian point of view. Saying an event is not only unequivocally bad, but also the most bad, is kinda... Impossible. I hope this gave you some perspective, even if it didn't answer your question.