Rebellion is the theme in new documentaries about the ‘Persian Picasso’ and the man who inspired Dog Day Afternoon. Critic Owen Gleiberman gives his review.

Remember when it actually meant something to be a rebel? These days, it would be hard to think of a word that has grown more empty and annoying in its self-satisfied ubiquity. To brand yourself a rebel once meant that you stood against the complacency of middle-class values and flew in the face of the consumer culture. Today, though, rebellion is a brand: it's the clothes you wear, the tattoos you flaunt, the viral underground catchphrases you spout at the office and the tone of dismissive nonchalance you strike on Facebook. To be a rebel now means selling yourself as someone who won't sell yourself.

But two galvanising new documentaries take us back to a time when rebellion wasn't just cool but threatening. John Wojtowicz, the title badass of The Dog, is the man on whom the Al Pacino character in Dog Day Afternoon was based, and when you see his real story unfold, you realise that it's even more radical – more recklessly sociopathic, crazy in its daring and tattered with nobility – than the one told in Sidney Lumet’s film. Bahman Mohassess, the central figure in Fifi Howls From Happiness, is the once-celebrated, long-vanished ‘Persian Picasso’, who was an important artistic figure in pre-Revolutionary Iran. When director Mitra Farahani tracks him down in an anonymous hotel room in Rome, she finds a man so consumed by the purity of his passion that it's like a toxic flame that threatens to engulf him; he has even destroyed most of his paintings. In The Dog and Fifi Howls From Happiness, rebellion – the real thing – lives on, but as a shock force of creative destruction.

When Dog Day Afternoon was released in 1975, Lumet's true-life pressure-cooker tale of a Brooklyn bank robbery gone spectacularly wrong was justly hailed as an instant classic of the New Hollywood. The Dog shows you that Lumet's film got just about everything right, from the slipshod, hilariously unplanned details of the crime to the wormy, conflicted soul of John Wojtowicz, who masterminded the robbery because he needed money to pay for his lover's sex change operation. Depicting that relationship as frankly as it did, without laughs or condescension, made Dog Day Afternoon a revolutionary movie. No Hollywood star of the magnitude of Pacino had ever portrayed a homosexual character before. Yet the relationship between Pacino's live-wire Sonny and Chris Sarandon's clingy, forlorn, droopy-eyed Leon still played as a kind of jaw-dropping quirk, a bizarre embellishment of the central character's basic desperation.

A Dog’s life

The Dog puts the story in a new context by depicting Wojtowicz, from the start, as a gay man out of time – and, in fact, as someone who was way ahead of his time, because he wasn't going to let anything stand in the way of his desire to be with the man he loved. The real Wojtowicz appears before us brash and unrepentant, a Brooklyn spark plug with a thick New York accent and a finger-jabbing attitude to match. He's such an in-your-face working-class roughneck that almost nothing in his demeanor suggests he is gay, and that's part of what makes his story so bracing.

The Dog’s co-directors, Allison Berg and Frank Keraudren, have constructed their film with a crafty tabloid urgency, exploiting our knowledge of Dog Day Afternoon to present Wojtowicz as an even more oddball figure than we were expecting. The film keeps you riveted, yet its achievement is finally more humanistic than cinematic. Wojtowicz discovers his sexuality during Vietnam, through liaisons with other servicemen, and by the time he’s back from the war, the gay liberation movement is kicking off, and he becomes part of it. It’s astonishing to see video footage of Wojtowicz in the post-Stonewall Riot days, because his pugnacity at once heightens and undermines the morality of early gay politics.

That he chose in 1971 to marry his lover, Ernie (the real Leon), now looks heroic rather than eccentric. Ernie, in his prime, was beautiful enough to be a Warhol Superstar, and if robbing a bank to pay for his sex change sounds hard to justify, the full story actually makes a lot more sense. In reality, Wojtowicz didn't want Ernie to get the operation; the issue was ripping their relationship apart. He may also have been looking to pay off mob loans. But Ernie kept threatening to kill himself unless he could have the surgery, so as Wojtowicz saw it,  he robbed a bank in order to save Ernie's life. And that starts to look like the kind of recklessly devoted action that can tear our sympathies in two directions at once. Wojtowicz spent years living off his moment of infamy, a media-age irony at once triumphant and sad. "I'm the gay Babe Ruth," says Wojtowicz, his eyes a-twinkle. "I hit a home run. Know why I hit a home run? Because I beat the system. I won. Ernie got the sex change. Ernie survived. And I'm happy for that." Spoken like a rebel with a true, cracked cause: someone who never gave a thought to letting common sense get in the way of what he believed was right.

Destroyer of works

If Wojtowicz beat ‘the system’, then Bahman Mohassess, the remarkable subject of Fifi Howls From Happiness, was eaten up and spit out by it. A product of the Iranian aristocracy, he rebelled in the most lacerating way possible, attempting to annihilate his identity as an artist before others could do it for him. You don’t have to be a modern-art aficionado to see that Mohassess is anintoxicating painter. One of his signature works – it gives Fifi Howls From Happiness its title – hangs in the hotel suite that he virtually never left before his death in 2010, and it depicts a red-headed figure with a hole where its face should be. It's a gorgeously scary image that suggests Munch's The Scream as repainted by Francis Bacon.

Mohassess calls the loss of human identity his theme, but it's a perception that has left him swimming in rage. He hates the Shah's Iran that celebrated his work but also repressed it; he hates the Iran of the 1979 Revolution that exiled him; he hates dictatorship; he hates democracy. Yet the man we see, who exudes a hacking giggle between chain-smoker's coughs, is an imp of irascibility, nostalgic for all the boys he slept with, and as uncompromising in his erotic passions as John Wojtowicz ("The most devastating thing they've done," Mohassess says, "is to eradicate the forbidden character of homosexuality.") Farahani’s direction is artfully suggestive but also, at moments, oblique; she seems to think that she’s making a Godardian essay-film. Yet if Fifi Howls From Happiness is a little ragged and pretentious around the edges, it’s mostly fascinating in its rapt gaze, and it allows us to revel in dozens of images of Mohassess' works, which commanded major prices before he destroyed them.His attack upon the beauty he created marks him as a uniquely compelling martyr of protest: a great artist who decided to let his creations live on in a half-remembered dream rather than die by being consumed.

The Dog: ★★★★☆

Fifi Howls From Happiness: ★★★☆☆

If you would like to comment on this story or anything else you have seen on BBC Culture, head over to our Facebook page or message us on Twitter.