As the two religions share the same template (holy books, one god, prophets and war on heretics), I think it is important to ask the reasons for the similarities.
Your comparative religions course might know Campbell, but it doesn't know Yahweh.
“One had the European culture overlaid on it and the other has the Arab culture overlaid on it.”
WHOA!
WHOA!
WHOA!
WHAT built classic “European culture”?
It was Jesus Christ teaching Europe through the Bible!!!
WHAT built classic “Arab culture”???
It was Mohammed teaching Arabia through the KORAN!!!
Jesus REDEEMED European culture.
Mohammed further DEGRADED Arabic culture.
Through your lens, maybe. For the Christian, the Bible is to be looked at as a whole revelation , as a mans life must be. The true image of God is Jesus Christ. Mohammed fastened on the image of God as understood by desert Jews, and he was himself a man of the desert. Like the old Sadducees, he accepted the Torah alone. Even the pharisees with whom Jesus clashed, went far beyond this understanding. The teachings of Jesus about God did not spring from the void, but are anticipated in the wisdom books—many of which btw are not in the Protestant Bible. I invite you to read Sirach.
It seems your knowledge of the Bible and of the Koran (and assoc. hadiths), or one of the two, is sorely lacking. ANYONE who reads both will immediately be impressed by the diametric opposition in them being juxtaposed. There is not only virtually no agreement between the two, they are EXACT opposites of each the other.
The 'god' Allah is *NOT* Almighty YHWH.