The Assyrian Empire and the Persian Empire were two of the earliest major empires in the world. The Assyrians were powerful from about 900 to about 600 BC. The Persian Empire came afterwards, holding power beginning around 550 BC. Both were empires in what we now call the Middle East. Both were monarchies. However, there were very important differences between the two.
A good way to express these differences is to say that, from our perspective, the Persian Empire was more enlightened. Because of this, it was possible for them to rule a much larger empire than the Assyrians could. The Assyrians had a much more autocratic and centralized system of government. The king of Assyria was seen as all-powerful. Everyone else in their society was seen as a slave of the king. When the Assyrians conquered other peoples, they tried to dominate them and exploit them. The Assyrians essentially used the outer parts of their kingdom as colonies to be exploited, not as valued parts of their own society.
By contrast, the Persian Empire was more enlightened. The king did not portray himself as a completely dominant figure. The people of the empire were portrayed as strong and important members of society. The empire was not exploited as ruthlessly for the benefit of the center. Instead, each part of the empire had its own governor and was seen as an equal part of the empire. Tribute was demanded from each region, but not as ruthlessly as in the Assyrian Empire.
Thus, the Assyrians and the Persians were both empires, but they ran in rather different ways.