In short Abbasid dynasty was sunni Muslim caliphate, Fatimids was shia Muslim caliphate, Ayyubids were secular rulers in sense that they did not claim caliphate. Both Abbasids and Fatimids were very enlightened empires of the period. There is not much difference between them because all three were Arabic/Middle Eastern Islamic dynasties but if you compare these three to other Islamic dynaties in India, Central Asia and Turkic Islamic dynasties you will find many differences.