Facebook, so far as I've come to experience it, is intended more for sharing and/or communicating ideas, thoughts, photos, videos, etc. of any social topic imaginable.
LinkedIn, on the other hand, is intended more for the professional in the work force. LinkedIn is designed to be used as a professional networking tool. Through this professional level of networking, employers and recruiters are able to seek out information on potential employees. For some LinkedIn account holders, they use this as an electronic business card or resume displaying customized information such as education, recent employment, recommendations, unique skills, etc.
Although both are unique in their intended purposes, both Facebook and LinkedIn, allow account holders to set their privacy preferences and allow users to display whatever information they would like to be seen either by a select group of friends or contacts, or publicly by the vast users of the Internet.