Shakespeare hits the nail on the head on the subject of war when he has the jealous Othello bid his emotional farewell to “big wars that make ambition virtue!”. It is not ambition alone that gets turned into something else by war. Viewpoints become causes. Murderousness becomes strength of purpose. A pointless death becomes a national sacrifice. The most terrible thing about wars is not that they happen, but that in starting them, we alter the DNA of our values.

I kept having dark thoughts like these as I poked my way around the Barbican’s compelling yet dismaying investigation of war photography in general and Robert Capa’s in particular. Downstairs at the Barbican, contemporary artists from Israel, Vietnam and Holland are seen tackling the current wars in the Middle East, with intriguing results. Upstairs, Capa spends 1936 rampaging through the Spanish civil war and still has enough fight hormones coursing through his upstanding veins to rampage through the D-day landings in 1944. In Spain, he is joined by his notable girlfriend and fellow war photographer Gerda Taro, who has also been given a show to herself here. Taro was killed in 1937 at the Battle of Brunete. So Capa spends the rest of his action-packed career partnered flimsily by adrenaline and glory. In 1954, he stepped on a roadside mine at a small turn-off in the first Indochina war, and died the death he seemed always to have been angling for. Oh, and in between he founded Magnum Photos, that alpha-male photographers’ club that still calls so many of the photographic shots in modern media.

It’s a truly remarkable story, but truth itself gets outflanked by it. Capa’s real name was Endre Erno Friedmann. He was born in Hungary in 1913, a left-leaning Jew who wanted to make a difference. His first ambition was to be a writer, but he fell into photography and discovered he could write compelling fictions in that medium as well. In 1936, he changed his name to Robert Capa, because he thought it sounded more American and because he admired the film director Frank Capra. In Hungarian, Capa means shark. So, Bob Shark it was, international seeker of trouble zones and war buzzes.

A few months into this career, Capa headed for Spain, where he instinctively supported the Republican cause against Franco’s fascists. And on the morning of September 5, 1936, he found himself embedded with a squad of loyalist soldiers on the southern front line in Cordoba. We will never know exactly what happened next, but by the end of it, Capa had taken the most famous war photograph of them all, a blurry view of a loyalist hero being shot on a hillside in an image that has come to be known as the Falling Soldier.

I need to admit I went into this exhibition believing this famous photograph to have been faked. I am not alone. Assorted doubting voices have long been raised, disbelieving that Capa could have been in exactly the right place for exactly this moment. However, heavyweight research completed recently in Spain appears to confirm that a certain Federico Borrell Garcia was indeed killed outside Cordoba in the skirmish in question, and that Capa was indeed able to witness his death. So that should have been that. The world’s most famous war photograph should have been what it seemed to be.

Instead, the Barbican show manages to knot these ethical complexities still tighter by suggesting yet another story line. It now seems possible that Capa was deliberately posing the loyalist militia on the day in question. But while asking Garcia to stand before him and appear indomitable, Capa managed to attract the attention of the watching fascists, who shot Garcia as Capa was posing him. Which is why his camera was so preternaturally ready. The true story could therefore be that Capa himself created the circumstances in which Garcia was killed.

The show re-creates several of his most celebrated photo stories and allows us to see how they were assembled. And it reveals how Capa’s growing legend began to play a crucial role in the shaping of his impact. In 1938, Picture Post was already declaring him the “greatest war photographer in the world” and showing him, in Taro’s rousing portrait, as a swarthy, swashbuckling adventurer. The little Hungarian did a very passable impersonation of a matinée idol. (Taro’s real name, by the way, was Gerda Pohorylle. She took Taro from the Japanese artist Taro Okamoto, and the cadence of the whole from Greta Garbo. At first, the two of them worked together as “Robert Capa”. Only later did Friedmann claim the name for himself.)

Apart from warning us never to trust war photography, the most valuable thing the show does is to highlight the role played by magazine editors and designers in the creation of the Capa myth. The difference in impact between the negatives Capa sent in and the photo spreads created from them by Life or Picture Post or Paris Match is startling. The finest example is the suite of D-day pictures that constitute Capa’s second-best-known work. Landing on Omaha beach with the Americans, he shot four rolls of floundering GIs bobbing about in the treacherous waters. Three and a half of these rolls were later destroyed in a darkroom accident; the 11 remaining negatives were all Life magazine had to play with. But the resulting picture story is a brilliant action layout.

Taking the quietest of Capa’s D-day pictures as a scene-setter, Life’s designers have you turning the page into blurred, shocking mayhem. It’s impossible to tell what constitutes shaky action photography and what is due to the darkroom disaster, but the results are violently eloquent.

An even clearer example of the part played by Life’s dramatists is the famous cover from the Sino-Japanese war of 1938, on which a 15-year-old Chinese soldier stares sternly into his future. Here, the designers airbrushed out the distracting building hovering over the soldier’s shoulder in the original and focused all the attention on his shadowy face. The striking red typography of the Life masthead completes the effect.

So, there’s an awful lot of simulation involved in a survey that ends up asking more questions than it answers. For a clearer exposition of war photography’s essential dilemmas, I recommend the contemporary show downstairs. None of these younger photographers is blinded by the adrenaline rushes that distinguish Capa, and perhaps invalidate him.

The best offering is a complex piece of elucidation created by the Israeli artist Omer Fast, whose two-screen projection tells the story of an American soldier who accidentally kills a civilian on a road in Iraq. The drama unfolds brilliantly through simulated freeze frames involving actors in real time pretending they cannot move as Fast weaves in a parallel tale of the same GI encountering a self-harming German girl at his European base. The two meetings with strangers mix the personal and the historical in an eerie cocktail. When you walk round to the back of the piece, a third scenario awaits you. The voice you have been listening to is being edited together as you watch, from fragments of interview set at different times and different places. The whole experience is revealed as a carefully edited concoction. That’s war photography for you.

This Is War! is at the Barbican, EC2, until January 25

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