Apart from minor matters of punctuation and style, there are changes such as “Observe” instead of “Remember” the beginning of the Sabbath commandment; the reason for Shabbat has to do with the emergence from slavery, not the creation; an extra clause is added to the law about honouring parents; and there are differences in the commandment about not coveting.
The earlier version, found in Sh’mot chapter 20, is more celebrated, but who is to judge which version is more authoritative?
An associated question: if the first Decalogue came via the hands of Moses, was the second Decalogue transmitted by someone else?
Dr Aron Barth, in an important book called Dorenu Mul She’elot HaNetzach – “Our Generation Facing Eternal Problems”, argues that no-one else would have had the impertinence to alter the first version. Only Moses would feel confident enough to adapt and expand the commandments and to add new emphases for a later generation.
As the pioneer of the rabbinic profession Moses would have understood how rabbis in every age felt it necessary to stress particular aspects of Judaism.
Maimonides, for example, produced a series of great works of philosophy in which he gave Jewish belief a rational basis as against those who emphasised the emotional and passionate dimensions. Only because Maimonides and the rabbis knew that they were authorised by their ordination to transmit the Torah to their own generation could they feel comfortable in seeming to adapt the content of the tradition.
In Moses’ case there could be no problem. Moses, above all other rabbis and teachers, could use the material almost like a potter shaping his potsherd (cf. the Yom Kippur poem, Ki Hinneh KaChomer, which describes God as a potter who shapes the raw material of the world).