When the Germanic kings replaced the Roman emperors as rulers of Italy, when barbarians from the steppes - be they Manchu or Mongol - put one of their own on the throne of the ancient empire to their south, they largely adopted the customs and languages of the peoples they conquered, to varying degrees. On the other hand, the peoples of Anatolia and Pannonia adopted the culture of their Hungarian and Turkish conquerors, and the Middle East and North Africa were thoroughly Arabized over the course of just a few centuries.
What are the deciding factors in whether a minority of conquerors will adopt the culture of the peoples they conquered, or impose their own culture on their new lands, and what such processes could've gone differently? Would it be possible for those Alemannians and Bavarians that found themselves on the opposide side of the Alps to their own to adopt the language of the peoples of Raetia and Noricum, for example?