In fact, the Crusades were directly a result of the Turkish invasion - in particular, the destruction of the Byzantine army at Manzikert, which resulted in the loss of much of Anatolia - the Byzantine heartland. There is abundant historical testament to this fact; entreaties from Byzantine emperors to the Pope, kings, etc. The First Crusade was explicitly an answer to these calls.
Any relation to the Moorish conquest of Spain, 300 years earlier, is at the very best, indirect. In fact, it is so indirect as to be non-existent. What it really meant was that Spain didn't involve itself in the Crusades.
I agree that Muslims, as a whole, were more aggressive than Christians for much of the time since Mohammed. Islam was a militant religion, spread by the sword. That started from the very beginning of Islam. Mohammed himself led the charge, as it were. It is an essential part of Islamic creed that the whole world must be converted to Islam, forcibly. And de-conversion is punishable by death. It is a highly virulent religion.
Of course, Christianity was spread by militarism, too. It started with Constantine (400 years after the religion was founded): as soon as Christianity became the State religion, it began to be imposed on the mostly pagan population of the Empire, increasingly, over a period of decades. Eventually, Roman successors (e.g. Charlemagne) imposed Christianity at the point of the sword on other native populations (e.g. Germans). All across Europe, Christianity was imposed by the force of the state. This continued as late as the year 1,000, when Iceland was converted. It continued, of course, with the Crusades - very explicitly, a campaign to conquer the Holy Land, to re-impose Christianity on it (largely by killing or driving out the inhabitants and replacing them with Christian colonists). That takes us to about 1,200, when they were driven out. It continued with the conquering of the New World, beginning in the 1500's, as Native Americans were forced to convert at the point of the sword (especially by the Spaniards).
But I would agree that Islam was (and still is) far more militant, as a religion, than Christianity, at any given time. Christianity has largely been de-fanged (and is slowly disappearing, as a result). Islam has not been defanged, and is still spreading. But keep in mind that both Christianity and Islam have been spread mostly by military, or state, force.