Easy: A mission statement is usually boring and completed as a corporate project, complete with consultants and other things that ultimately water the whole thing down.
A manifesto is usually completed by an individual and looks to throw fastballs at the head of the establishment. Manifestos can't make it through a group editing process because they're too renegade.
Mission statements are the opiate of the masses. Marx thought it was religion - it's not - mission statements are the crackpipe of the corporate masses.
Jerry McGuire called what he did a mission statement. It was actually a manifesto. He got fired as a result (I'm here to fire you Jerry. Could you stop thinking about yourself all the time?). The manifesto was too big for "the man".
Reference - this post on manifestos over at The Cynical Girl, with specific reference to the comment by "Jackie".