Kenneth Branagh’s new adaptation of “Murder on the Orient Express” contains some of the best of old and new. Based on the novel by Agatha Christie, this is in many ways an old-fashioned entertainment, but it has the pace and visual richness of a modern movie. And it’s almost as star-studded as the famous 1974 adaptation, which starred Albert Finney, Sean Connery, Ingrid Bergman (in an Oscar-winning performance), Lauren Bacall and John Gielgud.

Fans of the 1974 version may see this movie and think, “Oh, but the original was so much better.” But to them must go the question, “Yes, but when was the last time you saw that original?” — because this Branagh version makes an honest case for itself, with a flashy opening and an improved ending. Roles are beefed up, tailored to the strengths of particular actors. This is especially true in the case of Michelle Pfeiffer, who has a remarkable scene not found in the 1974 movie.

And then there’s Branagh himself as the Belgian detective Hercule Poirot, who enters into a struggle with an elaborate and highly distracting mustache and ultimately emerges victorious. It’s a close call. The mustache is a fascinating work of engineering, extending across most of his face, and for at least the first half hour, it distracts from dialogue at every close-up. But Branagh wins out through charm and a general sense of fun that doesn’t preclude an underlying sadness.

The Poirot of Branagh is an oddball — Poirots are often oddballs — but this time he isn’t all that happy about life as an outsider. He explains that he has an obsession with perfection that makes daily life difficult, but that allows him to see imperfections, or clues, that others miss. Exhausted by overwork, he boards a train for the beginning of a vacation, but, alas, when you’re Hercule Poirot, murders have a way of just happening.

He’s not on the train for two hours before a businessman named Ratchett tries to hire him as a kind of bodyguard. Johnny Depp plays Ratchett, and for the first time in several years, Depp doesn’t mug. Instead, he subtly exudes spiritual wrongness. He’s polite. He speaks softly, but you just know, something isn’t right with this guy. And if we can tell, so can Poirot, who turns him down flat.

Soon, a murder is committed, and by an apparently confident murderer, too, considering that the greatest detective in the world happens to be in the same train car. Poirot takes over the investigation, which allows Branagh to give himself close-ups while saying things like, “There’s a murderer among us!”

Though the 1974 film could have been adapted into a stage play, with almost every scene taking place inside the train, Branagh opens things up to good effect. For one thing, the movie begins in Jerusalem, with Poirot solving a case while standing in front of the Wailing Wall. The wintry vistas outside the train are lush and gorgeous, and even when the train derails in the snow, Branagh finds ways to take scenes outside.

One might think that a sense of claustrophobia might actually work to the advantage of a murder mystery, but by making his movie beautiful, Branagh serves another purpose. He gives it the glow of the distant past — it’s set in 1934 — and makes everything a little more intense, and slightly unreal.

By the way, for fans of the original film who want to know who plays whom, Derek Jacoby has the Sir John Gielgud role; Penelope Cruz is the missionary played by Ingrid Bergman; Josh Gad is the shady secretary originally played by Anthony Perkins (totally different vibe, but equally good); and Judi Dench is the Princess Dragomiroff, originally played by Wendy Hiller.

But the most interesting bit of casting is Michelle Pfeiffer as Caroline, the divorcee originally played by Lauren Bacall. It’s easy to forget, because she’s so down-to-earth, but Pfeiffer is a great screen actress — not just good, or very good, or interesting, but genuinely great, as in one of the best we have. In writing this adaptation, Michael Green apparently understood this, and gave Pfeiffer a chance to hit one out of the park.

One doesn’t expect that kind of intensity in a sedate British murder mystery, but Pfeiffer brings it. On her own, she helps Branagh make the case for his remake over the original.