to debate -- I wonder if that is always true -- after all the Moslem hordes invaded and took over the higher civilisations of India, Iran
Persia is an unusual case, because it is the crossroads of southern Asia, as Turkey is the meeting point between Asia and Europe. Both have been frequently overrun.
The first conquest of Persia was by Alexander, then with the end of his empire, they were dominated by Greece for a while longer, during which both Zoroastrianism and Buddhism held sway. Though the Arabic conquest at the time was fierce, it was only partially successful, as the Persians could not abide dominance by Arabs, to the point of creating the great schism of Islam, becoming the Shiites. The Zoroastarians still dominated the upper classes to modern times, with Islam being the religion of the poor.
India was even more haphazard, Islam having only limited force, and meeting a brick wall of Hindu and Buddhism. For a long time there was coexistence, with various kings vying for which religion would be more advantageous. The last example of this was in modern Kashmir, in which the king refused to choose, resulting in contention that exists to this day.
A similar thing happened with the Islamic conquest of western Europe from Africa. Almost making it to France before being turned back, there was generally modest to moderate instability with Christians until the Muslims were finally booted out during the Reconquista in 1492.
Yet during all of this, determining which force was *more* civilized is problematic. They were not profoundly different, a choice between civilization and barbarity, as were the (western) Romans and the tribes of Gaul, so the contention was more between equals.
And this is a great example of barbarism vs. the decline of civilization. It took a very long time for the tribes to conquer the western Roman empire, and in that time they had become far more civilized.