Mostly because the Islamic faith has a much stronger grip on society than Christianity had.
Even by the end of the Middle Ages, the contestation of the Church was active in Europe in ways much greater than anything existing today in the Muslim world. It flourished during the Enlightenment, and Hume or Voltaire have no equivalent in the Muslim world today (where you still have religious figures arguing the earth is flat because the Quran says so).
As a consequence, the Muslim GDP/head which was superior to the western GDP per head in the year 1000 reached parity circa 1300 and was left way behind by 1500-1600.
Nothing to do with the USA, all to do with the economy and religion.
Edit: on another point you make, you greatly underestimate the historical Muslim internal strife
Just look at the history of Muslim rule in Spain as an extreme example. On a greater scale, the caliphal succession wars. Or the Shia/Sunni conflicts in History.