The difference between Dominican, Franciscan and Carmelite Spirituality
Dominicans have a much more bookish spirituality. They were a preaching reform movement that was focused on academic and intellectual renewal. They were formidable debaters and made their mark in making the gospel accessible to the common man in forms and words they could understand.
Franciscans came from St. Francis who was more pastoral. He wanted reform, but wanted more peace and harmony with nature, solidarity with the poor, being contrary to clerical privilege, etc. It was certainly more evangelical in flavor. They were more about preaching the truth through works and example and not so much in preachy words and erudite theologizing.
Carmelites are much more contemplative, interior prayer, contemplation of holy mysteries, interior life, etc. It is more focused on the inward spiritual journey. It is rooted in the life of Elijah the prophet (on the original Mount Carmel in Israel, which is a beautiful place to visit), when he went to the mountain and finally found God not in the fire or storm or rushing wind, but in a tiny quiet whisper.