Since most modern wars were fought over natural resources, I assume the world wars of Jupiter would come much later. Technology could have advanced :
-slower because people have more living room
-faster because there are more people thus more discoveries
I would say we would know all about Jupiter's land and islands, but there would be plenty of uninhabited parts. Imagine an ICBM needs 2-3 hours to reach their target here on Earth, there it could be 20+ hours, thus plenty of time to prepare for a nuclear attack.
Also because of the much larger size, we wouldn't need to worry about peak oil or such, although we have to assume that population will eventually explode there too. If the Earth comfortable carrying capacity is 6-9 billion, on Jupiter this would be 500 billion easily!
Size generally slows down things, but eventually the exponential growth of everything (discoveries,population, use of land and nat. resources) catches up.
It is safe to say there would be bigger technological differences, like one part living in the XX century, the other one still in the stoneage or before....
Assuming that the size protects from one giant tidal wave messing up all coastline life or the dinosauruses, there could be different lifeforms developing/surviving parallel. Imagine if a Jupiter oceancrossing would take 10 times more than on Earth! What are the chances Colombus would have survived it? Thus it would be probable that new continents were discovered as late as the mid-XX century. (probably by satelites not by planes!)