The Arbs beat the Persians ~ most through the hiring of Eastern Empire legions, but it was Arab money, Arab military strategy, and Arab leadership.
What you are forgetting is that a little event called The Dark Ages had begun circa 541 AD and destroyed the economy of most of Rome, as well as that of China, and a variety of other places. Western and Northern Europe were the most devastated. They were essentially abandoned for the next 500 years.
The Arabs pulled out of the Dark Ages in about 80 years, just like some of Byzantium. The Persians took a hit too, but they didn't have invading Slavs ~ just far less numerous Central Asians.
China, in contrast took 300 years to recover to the cultural and economic level it'd had in 540AD.
Western Europe took about 1000 years.
So, why did the Arabs in Mecca do in 80 years what took the folks in Western Europe 12 times as long?