What "argumentative thread" ran through the letters from 1815-1826 and how did each man view the French Revolution?

Which chapter are you referring to? 

chapter 6

During this period, Adams and Benjamin Rush, a longtime friend and fellow Founding Father, enjoyed a lively volley of correspondence. Their letters were existential and dream-like; Ellis describes them as “Adams and Rush in Wonderland” (214). Adams, ever mindful of posterity and certainly writing with the belief that his words would later be studied, recognized the difference between history as it is experienced, and history as it is remembered. In the correspondence, Adams considered how certain events of the Revolutionary period had become legendary, while others had been forgotten. 

Ellis believes that Jefferson had the unique ability to make himself believe anything, even when it was wrong. For instance, he supported the French Revolution until Napoleon revealed himself to be a dictator. Jefferson thought England would fall to France, but when facts proved otherwise, he was undaunted. Instead, he simply changed courses, and his political reputation did not suffer because of it. As a result, Jefferson became the illustrative hero of the Revolution, to himself and to the public. You can check more out at the link below: