Hollywood does not make films about depression-era gangsters very often. It is already two decades since De Palma’s Untouchables and Barry Levinson’s Bugsy. Arguably there are good reasons for this.

For one thing, the modern classics of the genre are so familiar that any new film featuring fedora hats, tommy guns and rounded cars with running boards is likely to feel ersatz and steeped in cliché. It may be that the period gangster film has become like the Western, a form that is all but exhausted except for the occasional “revisionist” treatment.

With Public Enemies, the superb, British-trained American filmmaker Michael Mann has tried to resuscitate the gangster movie in the way that Ridley Scott revived the sword and sandal epic with Gladiator — using modern technology and his trademark visual panache, and exploiting the appeal of Johnny Depp, one of today’s few genuine movie stars.

The result is a beautifully shot film with terrific, brilliantly crafted action sequences. It boasts a fine cast headed by one of the most glamorous male leads in Hollywood and lovely La Vie en Rose star Marion Cotillard.

It lovingly and painstakingly recreates the Depression era. Shot by cinematographer Dante Spinotti, it is no less visually gorgeous than any of Mann’s previous films and TV series, which include Heat, Last of the Mohicans and Collateral. Yet all this impeccable craft is let down by a jumbled storyline and inadequate characterisation.

The film celebrates the story of John Dillinger, the bank robber and folk hero, focusing on the blood-splattered 13-month heyday between his parole in May 1933 to his death in July 1934. For much of that time Dillinger and his gang was pursued by the nascent FBI, and in particular by special agent Melvin Purvis (Christian Bale), who also became a popular hero.

Though based on the groundbreaking book of the same name by Bryan Burrough, the film sticks to the traditional account of Dillinger’s betrayal by the “lady in red”, and makes Billie Frechette (Cotillard), a beautiful half-French, half Native-American hat-check girl, his exclusive lover.

Many of Mann’s best films are about two impressive men in mortal conflict — Al Pacino as the cop thwarting Robert de Niro’s armed robber in Heat, hitman Tom Cruise brought down by heroic cab driver Jamie Foxx in Collateral. A similar dynamic is clearly supposed to drive Public Enemies. However, the character of Purvis, Dillinger’s nemesis, is simply too opaque and too thin for the rivalry to have any dramatic power. Bale is never more than a jawline in a suit. It is not his fault — he is not given the lines necessary to establish a personality. It is not even clear if he is particularly good at his job, or if Dillinger and his gang are merely outwitting an incompetent.

This is all of a part with a general vagueness and confusion, as if the filmmakers were so entranced by gangster movie iconography and paraphernalia, or by the glamour of gun battles and Johnny Depp in a fedora, that they simply did not bother with the hard work of structuring a coherent and dramatically effective story.

It does not help that it is so hard to distinguish between the supporting gangsters. You can just about recognise the psychopathic Baby Face Nelson — who actually survived Dillinger by several months, contrary to the film — played by British Snatch star Stephen Graham. But the other members of the gang, even though they are played by well-known actors like Stephen Dorff and Giovanni Ribisi, are on screen too briefly and all look too much alike in their matching hats and coats.

Mann’s wonderful Last of the Mohicans, set in colonial America, was famous for its period accuracy in terms of firearms, clothing and manners. The director and his team have gone to similarly extraordinary efforts to make Public Enemies look and feel authentic. Much of it is filmed in the original locations — the Little Bohemia Lodge in Wisconsin; the Lake County Jail in Indiana, from which Dillinger made one of his most daring escapes; and the Biograph Theatre in Chicago, where he was killed.

However, you get no sense that in the real-life war between the gangsters and the forces of law and order — the latter were at a huge disadvantage. As Mann himself points out in the programme notes, there were only 27 state police in the whole of Indiana. The FBI at this early stage in its existence was a small, underfunded and under-equipped organisation whose agents had to borrow cars to chase after better-armed bank robbers driving the latest Ford V8S.

Its men — usually law school graduates — were even at a physical disadvantage compared to farm boys like John Dillinger, who had grown up doing heavy manual labour and could fire a machine gun weighing more than 20 lbs from the running board of a moving car with one hand.

Public Enemies also suffers from a lack of convictions. It tries to establish Dillinger as a good guy by showing him robbing banks but not individual customers, even though “the banks’ money” largely came from such customers.

But it is also happily untroubled by brutal violence, especially when the victims are cops, prison wardens or mere passers-by.

There were times when I wondered if the Public Enemies reflects Hollywood’s sense of the Iraq War in the same way that Bonnie and Clyde reflected feelings provoked by Vietnam and The Godfather series reflected cynicism inspired by Watergate — it is excited, righteous and generally confused.