In contrast to Edwards as "the Last Puritan," how does Benjamin Franklin in the dawn of the American Enlightenment represent the new Enlightenment generation that founded the US? What aspects are more or less attractive or admirable?

In order to approach this topic and to properly compare and contrast Jonathan Edwards and Benjamin Franklin, let us first establish some of the main principles of the two camps they represent: Puritanism and the Age of Enlightenment respectively.
Puritanism
This way of thinking is based on the beliefs of English Protestants in the late sixteenth and seventeenth centuries. Puritans believed in plainness and hard work—in the responsibility of the individual—and in the concept of a God who rewards and punishes.
Puritans also believed in literal interpretation of the Bible and in personal conversion.
Jonathan Edwards, an evangelical minister and theologian, embodied this philosophy in some ways, and in other ways, he represents a departure from traditional Puritanism (he called for unity in the church instead of intolerance, for example). He led the first "Great Awakening in America," a period of great revivalism, in the 1730s from his church in Northampton, Massachusetts.
What are Edwards's key messages? One is the importance of the individual. For Edwards and the Puritans, the responsibility for improvement rests on individual conversion and individual spiritual experience, not the building of a community. His best-known sermon is called "Sinners in the Hands of an Angry God." Here is an excerpt:

Thus it is that natural men are held in the hand of God, over the pit of hell; they have deserved the fiery pit, and are already sentenced to it; and God is dreadfully provoked, his anger is as great towards them as to those that are actually suffering the executions of the fierceness of his wrath in hell, and they have done nothing in the least to appease or abate that anger, neither is God in the least bound by any promise to hold them up one moment; the devil is waiting for them, hell is gaping for them, the flames gather and flash about them, and would fain lay hold on them, and swallow them up.

As we'll see below, this emphasis on the individual is a key difference between Puritanism and the Age of Reason.
Age of Enlightenment / Age of Reason
The Age of Reason centers around freedom of speech and individual rights. Proponents of this way of thinking were not interested in the afterlife, like the Puritans were, and they believed in a reasonable God. As opposed to focusing on "sinners" and "an Angry God," these thinkers assumed that people are basically good and decent.
Benjamin Franklin was a key figure in this movement. He pursued knowledge and enlightenment (and contributed major inventions to the fields of science and technology) not for his own personal prestige, but for the betterment of the society he lived in. This is a key point: the Age of Enlightenment was about the community, the free exchange of ideas, and the concept that teamwork could yield more significant results than individual endeavors.
"If a man empties his purse into his head, no one can take it away from him," Franklin once said. "An investment in knowledge always pays the best interest."
So, how did the Age of Enlightenment shape the founding of the United States? Our entire governmental structure is based on it. Consider the following: separation of church and state, a system of checks and balances, a Congress composed of many individuals that make decisions together. All of this is based on ideals that arose out of the Age of Enlightenment and not the Puritan way of thinking.
The question of which aspects of the Enlightenment generation are attractive or admirable is a matter of opinion: it is also something you will have to decide for yourself. However, you might consider the points in the paragraph above, which are reiterated below:
Community is more important than the individual.
Scientific advancements are for the benefit of everyone.
Teamwork is valued and varying opinions are welcome.
No one, not even the President, can make decisions unilaterally.
https://www.sciencefriday.com/articles/benjamin-franklin-americas-first-social-networker/