"God on our side" is in part a direct response to "The Patriot Game", e.g. "My name it is nothing, my age it means less" responds to "My name is O'Hanlon and I'm just gone sixteen". I'm not familiar with much of Dylan's output (must have led a sheltered life) but I'm sure I've seen references to others of his songs being partly based on previous songs. So new songs, but at least partly inspired by old ones, not merely re-using tunes.