The Babylon of Hammurabi is not the same as the later Babylon whose name would soon be laden with lustre and utter notoriety in later centuries; rather, this Babylon is still very much a new city, having only just been established a hundred years before and hitherto often a tributary to other powers, most notably the storied city-kingdom of Ur to the south.

 

Military-wise, Babylon itself is not very strong. It uses the weaker Spear and Skirmisher Levies along with Slingers, along with the usual Spearmen and Archers and Swordsmen in the early game along with the Onagers, transitioning later on to faster Light Chariots and tougher Guardsmen in the later stages of the game. Otherwise, it too has access to Semitic mercenaries which while decent, have low LOS, making them somewhat easy to intercept with spies.

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What Babylon has, however, are economic and cultural advantages that if played right, can cause it to skyrocket as a power. The first is its National Bonuses, which include most notably the ability to generate resources while its infantry units are out in the field. Next is its ability to build its first Wonder for free, and finally the ability to research all Policies for free at the Meeting House. 

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As a result, Babylon is best used as an all-rounder that relies on its army mainly for defence, whilst playing the long game - as Hammurabi historically did - build up your economy, then build the vast number of Wonders that are available for you until you are at a comfortable position where you can either think of winning through diplomacy, or using your vast resources to enhance your army further for obtaining a military victory.