There have been plenty of differences in the numerous Superman adaptations but maybe it's safe to say that the newest Superman film is the most different of all.
Probably the most obvious difference that we can see lies on the southern region of Mr. Clark Kent a.k.a. Superman. The trademark red underwear-ehem-shorts is glaringly gone.
This decision was done because the producers thought that modern times wouldn't normally accept this kind of fashion statement. For the sake of realism, they omitted one of Superman's trademark look.
But whether he's wearing it or not, his ability to save the world is what matters most. Although it helps that no more red shorts would draw our attention to that part of his anatomy.