"The son of Jack" is very informal. It's just not normally said. "Jack's son" sounds less stiff. Hope this helped!

'The son of Jack' is very formal and should only be used in formal documents, reports etc. 'Jack's son' is much more common and should in nearly all circumstances.

Modern: Jack's son Historical (or like in Game of Thrones): son of Jack (usually to describe or attribute lineage). For example, 1This is the genealogy of Jesus the Messiah the son of David, the son of Abraham: 2 Abraham was the father of Isaac, Isaac the father of Jacob, Jacob the father of Judah and his brothers, 3 Judah the father of Perez and Zerah, whose mother was Tamar, Perez the father of Hezron, Hezron the father of Ram [Matthew 1-3]