Muslim warriors were highly motivated because they believed they had a duty to convert others to their faith. The importance of this religious zeal for Muslim expansion cannot be overestimated. Alexander the Great's men, on the other hand, mutinied because they wished to return to Greece. Although Alexander was a phenomenal leader, he was not a god.
History has seen other military conquerors achieve rapid success, but their successes were often ephemeral. Alexander's empire did not survive him. Adolph Hitler's Third Reich and Napoleon's empire lasted less than fifteen years. But Islam was a potent and expansive force for many centuries. There were times when it seemed that Islam would overwhelm all of Christian Europe.
Islam's territorial growth was not just a result of military prowess. Jews and Christians living under Muslim rulers were allowed religious freedom. Also, the taxes they levied were usually not too onerous. The political entities that came from Islam (Umayyad, Abbasid, Ottoman, etc.) were formidable. Extensive and thriving trade networks linked remote territories.
There were few obstacles to Islam's spread for its first few centuries. The Byzantines were unable to contain the threat, and Constantinople nearly fell on several occasions. (Constantinople finally fell in 1453.) The Persians and Egyptians collapsed entirely, and both peoples converted to Islam.
Christian Europe belatedly met the Muslim threat with the Crusades and the Age of Exploration. The Crusades temporarily seized the Holy Land from Islam, while the Age of Exploration was motivated, at least in part, by the European desire to secure its own trade routes to Asia—without relying on Muslim middlemen.