Did the persians defeat the babylonians?

Yes, the Persians defeated the Babylonians. In 539 BCE, Cyrus the Great, the founder of the Achaemenid Empire, conquered Babylon, marking the end of the Neo-Babylonian Empire. This victory was significant and led to the establishment of Persian control over a vast territory, allowing Cyrus to implement policies that promoted tolerance and the return of exiled peoples, including the Jews, to their homelands.