Four years after Steve Jobs’s death, a new movie is reopening a debate over the Apple Inc. co-founder’s legacy.

Mr. Jobs’s allies, led by his widow, Laurene Powell Jobs, say the film “Steve Jobs,” and other recent depictions, play down his accomplishments and paint Mr. Jobs as cruel and inhumane. Ms. Jobs repeatedly tried to kill the film, according to people familiar with the conversations. She lobbied, among others, Sony Pictures Entertainment, which developed the script but passed on the movie for financial reasons, and...