Two very good movies with the same title...
The Mission (1986)
Directed by Roland Joffé. Starring Jeremy Irons, Robert De Niro, and Liam Neeson. Irons plays Father Gabriel, a Spanish Jesuit who goes to Brazil to build a mission in hopes that they will be able to convert the natives over to Christianity. De Niro plays Mendoza, a slave trader who seeks sanctuary with Gabriel after killing his brother in a fit of rage. They work together to successfully build the mission until Spain cedes the colony to Portugal who allow slave traders to round up natives. Mendoza organizes the natives in a resistance against Gabriel's wishes and all hell breaks loose.
It's a very beautiful movie, both in story and in the cinematography. Most people complain about how long the movie is but when it's filled with varying emotions, what could there be to complain about? Most people remember the movie poster which captures a scene in which a missionary is tied to a cross and sent over a waterfall.
The Mission (1999)
Directed by Johnny To. Starring Anthony Wong, Francis Ng, Simon Yam, and Eddy Ko. The movie centers on several bodyguards who are assigned to protect a triad member from being killed after receiving threats. One of the best action movies coming out of Hong Kong, this is viewed by many as the beginning of a millenial new wave in Hong Kong film. If you're looking for fancy action, watch John Woo (not that there's anything wrong with it). If you're looking for gritty and more realistic play, see this movie.