The Crusades petered out due to lack of funding. I don't think you could consider them to be being purchased with faith. Besides, Jihad is ongoing today. The Crusades began and ended within a 400 year period.
I wasn't going to touch this, and I am not muslim, but...
...Jihad, from my understanding, is a "personal struggle". It's a spiritualistic quest within. I understand from the western outside understanding it comes to exclusively mean "holy war", but that is a very small aspect of the greater responsibility of being a devout muslim.
People are bent daily by others using religion to beat them about the heads. Islam is a religion of peace, regardless of what a few thousand people have done to tarnish it and make the world believe.
CRUSADES
...were hardly a "holy war". As the above example it was a poor representation of religion as a whole, and it was hardly "holy". Yes it was sanctioned by the church, but only to give clemency to the tens of thousands of criminals that filled the ranks. It was an attempt by the universal church to cease in-fighting between european powers, giving them a target they could all hate. It was a greedy land grab propagated by murder, deceit, vandalism and worse...genocide.
HOLY WARRIORS
When I think of "holy warriors" honestly the first classic examples that come to mind are the Hebrews/Jews. From Jericho to the Macabees to the Sicarii combating Roman/Sassanid influence, when "only God should be in charge". Read about them sometime and notice the interesting parallels modernly we attribute Jihad.