How did European motivations for expansion compare to those of the Roman Empire, the Arab world under Islam, or the Mongols in Central Asia?

The expansion of the European nations were mixed of the three empires stated above: God and religion like the Arabs, glory like the Romans and stability and wealth like the Mongols. First is that the European nations expands for gaining new converts for Christianity. Next is like the Romans, the European nations seek adventures and fame for their names and the country they served. Lastly, like the Mongols who in search of wealth and stability for their tribes, Europeans were in search of the wealth and resources that was lost after the fall of the Christian kingdoms like the crusader kingdoms and old trading partners in the Middle East.