How did the ten commandments differ from the laws of neighboring peoples?

The ten commandments is generally considered the core of what has become known as Mosaic Law. Mosaic Law is God centered: the central thought is that to break one of the 10 commandments is an affront to God and constitutes a sin not of a civil nature (as with the Hammurabi code), but a deeply spiritual and religious code. 

People have lived by the laws of Moses (and their all encompassing simplicity) for 3000 years, and although Hammurabi is older, it is less central. The idea of Hammurabi is that of punishment which is an eye for an eye and a tooth for a tooth. What is taken illegally must be returned.  The Ten Commandments are less concerned with punishment than with conducting a good and dutiful life. The Law (as the New Testament calls it) has to do with behavior and obedience which leads to righteousness. Punishment is sometimes spoken of, but most of the time it is about how God expects us to live a life that is beyond reproach.