The Islamic empire and the Mongol empire emerged as a result of prolonged and bloody military campaigns in many countries extending over a number of different regions. The Islamic empire made conquests from Spain in the West, to Central Asia in the East. The Mongol empire attacked many countries from Poland to Hungary in the West, to Korea and Japan in the East.
Both empires were relatively tolerant of other faiths, but Mongol empire was more pluralistic in regard to religion. The Islamic empire discriminated against non-Muslims while at the same time protected Christians, Jews, and Zoroastrians to some degree. Both empires were commercially oriented, albeit to varying degrees. The Mongols made a point of offering safety and security to foreign merchants to encourage their participation in international trade, which was very profitable to all parties.
Both empires stimulated cultural contacts and the exchange of knowledge and technology among various regions and civilizations. Paper, for example, originated in China and Islamic civilization spread it far and wide. The Mongol empire developed the first effective firearms by combining Eastern and Western metalworking technologies; other countries were quick to adopt this new weaponry.
While the Mongol empire was more tolerant of religious and cultural diversity, it was also more hostile to large urban centers of resistance. The Mongol armies wiped out masses of people in the cities of Central Asia, Iran, Iraq, and Russia. Much later, Tamerlane’s army destroyed Delhi and some important Middle Eastern cities together with much of their populations. The Mongol invasion contributed to the decline of urban settlements in Central Asia in the later Middle Ages.
The Islamic empire also spread the distinctive Islamic civilization, which had a deep and lasting impact on the conquered countries and transformed their culture forever. The Mongol civilization had a much more limited influence; China, the Middle East, and Russia preserved their cultural traditions relatively intact. While some early Mongol rulers became Christian, most of the later Mongol rulers converted to Islam and embraced its culture. At the same, however, Mongol domination generated fear and resentment among many Islamic scholars, such as Ibn Taimiyya, who continued to argue for jihad against Mongol rulers even after their conversion to Islam.
You should first note that there were several Islamic Empires, the two largest being the Umayyad and Abbasid Dynasties. The areas of Eurasia and Africa which became Islamic were known as the Dar Al Islam, the House of Islam. The Dar Al Islam occupied large portions of Spain and Northern Africa, and the Middle East. Other than Spain, Western Europe was largely unaffected. The Mongol Empire under Ghengis Khan was the largest the world has known, occupying China, the Middle East, and large portions of Russia to the edge of Western Europe. It's advance was only stopped by the death of Ogedai Khan. Trade was protected in both, although in the Islamic Empire, most trade was with Islamic Merchants. The Mongols were tolerant of religion, and took no position on religious practice. Islamic kingdoms did "protect" those who were considered "People of the Book," that is Christians and Jews, but they were forced to pay a tax. No other religions were tolerated in Islam.