We make the wrong analogy, comparing today's Islam with today's Christianity. Compare instead today's Islam with the Christianity of roughly 800 years ago and you find the comparisons you seek.
Today's mujaheedin or jihadists are very like the crusaders of the period of 1090 to 1290 and perhaps for 200 years more in Spain and eastern Europe. Crusaders fought against Islam to capture the "Holy Land" or Palestine for Christianity. They also recaptured Spain from the Islamic Moors.
Today's Al Qaeda and Taliban, Hamas and Hezbollah are rough analogs of the Knights of St. John, the Templars and Hospitallers, orders of religious fighters. Compare Osama ben Laden with Richard Lionheart, Balien or el Cid.
Muslims hate the memory of the Crusaders, with good reason. Oddly, they do not recognize as such the new crusaders in their midst.
