I always use "Have you seen ...?" when I'm talking about films, particularly if I'm asking someone about a film they might or might not have seen at some point in their lives. I would use "Did you watch ...?" for TV shows.
I might use "Did you see ...?" for films when talking about someone's specific visit to a cinema.
John: I went to the cinema last night?
Me: Did you [go and] see Star Wars or Bridget Jones' Diary?
John: Neither. We saw Interstellar.