Michael Mann’s Public Enemies begs a comparison to Heat, his masterful crime film starring Robert De Niro as a bank robber and Al Pacino as the cop who’s pursuing him. In Public Enemies, those roles are occupied by Johnny Depp (as John Dillinger) and Christian Bale (as FBI agent Melvin Purvis), along with a myriad B-cast that covers much the same range as the secondary players in Heat. It’s a shame, then, that Mr. Mann, who gave us such masterful characterization and intense action in Heat, can only give us a shallow and ultimately unsatisfying glimpse at the final exploits of Dillinger.

It isn’t as if there’s no good material to work with. Dillinger was a hero to the Depression-era working man, robbing banks and the federal government and always treating his hostages kindly. There was a brashness to him, too, as if he were one of the last Wild West bandits still thumbing his nose at the authorities in an increasingly standardized world.

His escapes were daring, not to mention improbable—they’d seem to be an invention of Mr. Mann’s (and fellow writers Ronan Bennett and Ann Biderman) if they hadn’t been so well-documented elsewhere. Who else would think to escape prison using a piece of soap carved into the shape of a gun? Who else would march right into prison with a fellow bandit dressed as an FBI agent, just to spring the rest of his gang?

There are plenty of subplots lurking, too, that hold much promise: guiding Purvis is none other than J. Edgar Hoover (Billy Crudup), who thinks finally nabbing Dillinger and his compatriots will allow him to turn the FBI into the fearsome bludgeon it would soon become. Likewise, the Chicago mobs, previously friendly to Dillinger, grow increasingly hostile as they realize the robber’s interstate crimes threaten to put their whole operation under federal scrutiny.

On a more intimate level, Dillinger’s relationship with coat check girl Billie (Marion Cotillard)—again, so similar to De Niro’s love interest in Heat—is just one more loose thread that could unravel his life. Intermittently, Dillinger’s deliberate cultivation of his public persona—and the celebrity that comes with it—both helps and hinders his spree.

All of this is good material barely glimpsed as we move, with the plodding certainty of a History Channel recreation, from one famous point in Dillinger’s life to the next. For Mr. Mann, it appears to be enough to suggest the complexities and themes at work without fully exploring (or even acknowledging) any of them.

This is most fully evident in the scant characterization. In short order we learn that Dillinger is cocky and doesn’t plan ahead, and that Purvis is a straight arrow. And though we will spend 140 minutes with them, we will learn little else. Mr. Depp and Mr. Bale are talented actors with natural presence, and that’s a good thing; without them their roles would be simple ciphers, guided by historical footnotes and devoid of real life. Ms. Cotillard isn’t given much to do but pine for Dillinger and stand nobly by his side.

If Public Enemies has one thing going for it, it’s in Mr. Mann’s beautifully understated cinematography. He’s been using digital film for his last handful of films as his subject matter leans gradually toward a more authentic, documentarian sensibility. Miami Vice, for all its glitz, simply pointed the camera and observed its players. There’s a beauty in that simplicity, and every shot is composed as if waiting for Edward Hopper to paint it.

That sensibility—to film “life as it is lived,“ no more and no less—is at play in Public Enemies, but in his desire to be hands-off and simply record Dillinger’s last days, Mr. Mann misses a chance at real drama. It’s fair for characters to play with their cards close to their chests; but here they are so impenetrable they are simply two-dimensional. Though blessed with gifted actors and a great historical premise, Public Enemies runs merely skin deep.