The three rulers share many aspects in common:
Strong government. Akbar, Shah Abbas, and Suleiman remained in power until their death. The three of them based their power in a strong army, which they used to expand their empires, and in the centralization of public administration. This, jointly with economic prosperity, allowed them to create a time of social and political stability.
Flourishing of art, science, and culture. Under their patronage, the three empires entered in a golden time of development of the arts and culture. In the Ottoman Empire, under Suleiman's rule, hundreds of artist communities were created, which used to combine artistic influences from Turkish, Islamic, and European origins. Suleiman himself was a poet and he created many schools and universities free for Muslim boys. Akbar created a library of over 24,000 books written in different languages, one library exclusive for women and many scholars, translators, and calligraphers from different religions and cultures were welcomed to study. Shah Abbas impulsed the creation of a school of painting, which created the finest Iranian paintings in its History, and also he enhanced the production of ceramic pottery.
Diplomacy. The three rulers were expert diplomats, which allowed them to make strategical alliances and negotiations with neighbor states in order to keep peace and the safety -and also the expansion- of their frontiers.
Reformers. The three rulers were also great reformers of their societies. Under Shah Abbas, the Mughal Empire experienced a syncretization of Persian, Indian, Islamic, Hindu and several other traditions. He created a new religion -or it should be called a political system- called Din-i Illahi, which attempted to bring unity in plurality. Suleiman, on the other hand, was a great legislator, he adapted the traditional laws to the new times, making them more tolerant with non-Muslims. Shah Abbas moved the capital of the Safavid Empire to Isfahan and reformed the army.
The differences can be seen mainly in how their power was limited by religious law.
Akbar was the head of the new state's religious and ethical system Din-i Illahi, even calling himself a prophet, which gave him a big personal power. He shares a similarity with Shah Abbas' absolute power. Since the Safavid emperor was the representative of the Imams he was not limited by the Islamic law, because he had both a temporal and spiritual power. This is very different from Suleiman, who was strictly limited by the Islamic law, as they were interpreted by the religious authorities.
