The ancient cities of Akkad and Babylon were both in Mesopotamia and located near the Tigris and Euphrates Rivers. They also spoke the same language (Akkadian) but with some regional differences, much as the North and South in the US have. Another good similarity is that they were both empires, ruled from a central seat of power by a single ruler.
When it comes to differences, the location of Babylon is known to this day, whereas there is no definite proof of exactly where Sargon’s capital of Akkad was. Babylon under Hammurabi was more of a society of laws than Akkad. Each had its own main deity, with the Mother Goddess in Akkad and Marduk in Babylon.
They had only 1 difference the Assyrians (Akkadians) were in the Northern Mesopotamia, and the Babylonians were in Southern Mesopotamia. They always had the same language, same laws, same mentalities, and the same religion.