Which empire defeated Babylon and came next in Nebuchadnezzar's dream?
The Mede and Persian Empire defeated Babylon and was the next kingdom after the head of gold. It was inferior to Babylon, though militarily greater, and instead of one absolute dictator, two kings, Darius and Cyrus, ruled and had to agree before any move.
Les explains that the head of gold was an absolute government under God, a government of one. Then comes the kingdom inferior to him. Politically, the next kingdom that defeated Babylon was the Mede and Persian Empire. Militarily they were already greater, otherwise they could never have defeated Babylon. But instead of an absolute dictator of one, there are two kings, Darius and Cyrus, the Medes and Persians, who had to agree before any military, economic, or political move. It's harder to get two people to agree than one. Then the next kingdom of brass shall bear rule over all the earth; secular history shows that was Alexander the Great of Greece. As soon as Alexander completed his conquest at age 33, he died, and his kingdom was divided between four generals.