question about the world being different without his discovery, I'm assuming you are talking about lightening being electricity. Although Franklin was a great mind, the scientific discoveries he made would have been made by others within a short time. There were a lot of people working with those ideas during these times, and the quick answer to your question is that without Franklin, some things would have been delayed, in the scientific areas, but the net effect for the present would be minimal.

If you refer to his place in politics, though, things could very well have been different without him. dbello, in post #2, hits on what I think are the more pivotal differences Franklin made.

Here's only 2 points from his remarkable life: Franklin is the reason we describe both static and current electricity as "positive" or "negative."  His observation that lightning appears to be a bigger version of the tiny electrical sparks he produced in his laboratory led him to prove that lightning was indeed electricity, and being so, he realized that grounding it would through lightning rods would save buildings from the risk of fire.  This may seem trivial to us, but in his day he had literally "stolen the god's thunder."  What had thought to have been the domain of the divine proved nothing more than a replicable natural phenomena.  As Postmaster General to the American Colonies, he was caught intercepting the mail and publishing its contents when he was attempting to influence the removal of the Massachusetts colonial governor following the Boston Tea Party.  A certain member of Parliament saw an opportunity to make a bid for Prime Minister, while concurrently destroying Franklin politically.  In January 1774, Franklin stood in a place known as the "Cock pit" where he endured a 2 hour censure.  Seeing that this was a ploy for political office rather than anything to do to attempt to resolve problems between Parliament and Colonies, he concluded that he, along with his countrymen, "must be Americans, for we can no longer be Britons."  Who had been an ardent supporter of Empire became equally an ardent supporter of Revolution, convincing many colonial leader to do the same.

Benjamin Franklin, Founding Father, signer of the Declaration of Independence, and a contributor to its content, he edited Thomas Jefferson's first draft, invented the concept of the library.  Creating the first lending library in Philadephia, he set in motion the ability of the common people to get access to books and education.  Dedicated to education, he started a small academy, which today is known as the University of Pennsylvania.

Further contributing to the foundational necessities of a prosperous and civilized society, he established the first hospital in Philadelphia, the idea of the Post Office, Fire Department and Police force all came from Franklin.

Franklin's experiments and innate curiosity about the nature of electricity furthered the study of the phenomena.  He invented the lightening rod, which helped buildings not be burned to the ground when stuck by lightening.  He also tried to harness the power of lightening and its relationship to electricity, conducting many experiments where electricity was funneled into his home through conductors.

Franklin was a great statesman, inventor and political philosopher.  His contributions to modern life range from the simple to the complex.

"in music, creating the glass harmonica for which Wolfgang Amadeus Mozart, Franz Joseph Haydn, and others wrote music;  he died the most beloved man in America and the most respected American in the world."