Rabbi Tzvi Elimelech of Dinov (Bnei Yissaschar, Chodesh Kislev, 2:25) explains that each exile was characterized by a different negative aspect:
The Babylonian exile was characterized by physical suffering and oppression. The Babylonians were lopsided toward the Sefirah of Gevurah, strength and bodily might.
The Persian exile was one of emotional temptation. The Persians were hedonists who declared that the purpose of life is to pursue indulgence and lusts—”Let us eat and drink, for tomorrow we may die.” They were lopsided toward the quality of Chessed, attraction and kindness (albeit to the self).
Hellenistic civilization was highly cultured and sophisticated. Although the Greeks had a strong sense of aesthetics, they were highly pompous, and viewed aesthetics as an end in itself. They were excessively attached to the quality of Tiferet, beauty. This was also related to an appreciation of the intellect’s transcendence over the body, which reveals the beauty of the spirit.
The exile of Edom began with Rome, whose culture lacked any clearly defined philosophy. Rather, it adopted the philosophies of all the preceding cultures, causing Roman culture to be in a constant flux. Although the Roman Empire has fallen, the Jews are still in the exile of Edom, and indeed, one can find this phenomenon of ever-changing trends dominating modern western society. The Romans and the various nations who inherited their rule (e.g., the Holy Roman Empire, the Europeans, the Americans) are lopsided toward Malchut, sovereignty, the lowest Sefirah, which can receive from any of the others, and act as a medium for them.