The Israelites and the Babylonians had more cultural differences than similarities. Their social structures were vastly different, as were their governments and religions. However, there are some similarities worth noting.
First of all, they employed similar technology. Having developed towards the end of the Bronze Age, they both employed the use of metal tools. Pastoralism and the farming of grain was practiced by both civilizations. They also developed sophisticated lunar calendars to plan and keep track of events such as holidays and harvests. Both had a week consisting of seven days (although the Babylonians also employed a five-day week in addition to the seven-day week).
The Babylonians and the Israelites spoke related languages. As part of the Semitic family of languages, Akkadian and Hebrew are closely related in syntax and grammar, meaning they would have sounded somewhat alike. Also, both were highly literate societies for their time, having produced a number of written records, many of which survive to this day.
Both the Israelites and the Babylonians had a written code of laws. The Babylonians are known for Hammurabi's Code, and the Israelites kept most of their laws in the Tanakh. These are some of the earliest known systems of codified law.
Finally, both were patriarchal societies in which men held political power and were in charge of family affairs.