One of the biggest differences is that Lex going from making zero sense (being an almost chaotic character) to making perfect sense. They make it clear that he's been pulling the strings and manipulating all sorts of things for years, for one. Secondly there's a couple of scenes inside the krypton Ian ship that suggest that he's gained some greater knowledge of what's "out there" - or possibly even communicated with / conspired with a powerful DC villain via the ship. His various motivations for destroying Superman (his complicated obsession with the nature of power is gone into in more depth, but also wanting to "clear the way" for aforementioned villain, which was completely missed out in the theatres).