Many of the differences between signed and spoken languages can be attributed to their different modalities: one makes use of our visual-gestural system, and the other of our aural-oral system. Differences in dexterity, processing time and other factors combine to create different modes of expression. I looked at these differences in my previous post on sign languages.
However, sign languages differ from languages like English in various other ways too. Most of these differences are sociolinguistic: social factors have a large impact on how we use language, and sign languages are no exception.