On the day in early 1969 when David Crosby, Stephen Stills and Graham Nash had their photograph taken for the cover of their first album together, they sat in line on an old sofa, radiating hippie allure and authenticity, outside a deserted house on a West Hollywood side street.

That evening, suddenly realising that they had posed in the wrong order (Nash, Stills, Crosby), they agreed to return the next day for a reshoot – only to discover that the house had been demolished overnight. As a metaphor for the destiny of what was, for a short time, the most popular rock group in the world, that would be hard to beat.

Within months, entropy arrived in the shape of Neil Young, who became the fourth member of the group – and its fourth highly developed ego. A brilliant but wilful and unreliable presence (or, more often, absence) with a parallel solo career, Young eventually exceeded the popularity of the original members to the point where the $60,000 available for a concert performance by the trio in a large stadium became $600,000 if his participation could be guaranteed. Not surprisingly, his decades-long show of reluctance to rejoin them created considerable resentment, particularly when there were yachts to be repaired, thoroughbreds to be stabled and drug habits to be funded.

The consequences of that ill feeling – the breakups and makeups, scandals over drugs and firearms, and a final backstage scuffle at, of all things, a Christmas tree-lighting ceremony at the White House in 2015, where they had performed “Silent Night” very badly in the presence of the Obamas and Miss Piggy – ensured that the group maintained some sort of public profile, even during their lengthy periods of inactivity. Peter Doggett, in the better of these two books, puts it neatly: “Crosby, Stills, Nash & Young have spent approximately two of the past 50 years as a functioning band and the other 48 years fending off questions about why they are no longer together.” Both he and David Browne, his rival author, strive to answer the question of how so brief and turbulent a heyday could have left so lasting an afterimage.

CSN&Y came together at a time when the music industry was overtaking films in Hollywood as the most prosperous and glamorous arm of show business. Its practitioners were encouraged to take advantage of all the personal and financial leeway this gave them. The musicians, rather than the men in suits, now called the shots – or so they believed. And they appeared at a moment of significant evolution in western culture, to which the critic Ellen Sander referred while welcoming their first album in the Saturday Review: “It is packed with songs of the changes that have made searchers of all of us.” Barely half a dozen years after the Beatles had introduced themselves with “Love Me Do” and “Please Please Me”, the scope of rock and roll had broadened; the topics of Vietnam-era political protest, ecological awareness and personal growth were all explicitly addressed by the four songwriters who pooled their work to create one of the first and certainly the most successful of the new generation of “supergroups”. Prefacing the era of the confessional first-person singer-songwriter (which, from James Taylor to Taylor Swift, continues to flourish), they provided their audience with the sense of being given access to a private and privileged world of exotic couplings and hip luxury.

At a time of hurtling progress, they were drawn together by musical ambition. Crosby had been sacked from the Byrds (for being a “little Hitler”, in a former colleague’s view); Nash had grown dissatisfied with the superficial pop music purveyed by his former group, the Hollies; and Stills and Young had been the most gifted members of Buffalo Springfield, an LA-based band which had been tipped for great things but failed to deliver. They were four children of damaged families – the sons, respectively, of the cameraman on High Noon, of an elusive figure who made and lost several fortunes while hauling his family around the southern states and Central America, of a Manchester steel worker and of a Canadian newspaper columnist. And they found each other amid the growing musical community of Laurel Canyon, in the Hollywood Hills, where the original three discovered, with the encouragement of such friends as Joni Mitchell and Mama Cass Elliot, that when they sang harmonies together, one plus one plus one equalled more than three.

Rumours of their project provoked great excitement on both sides of the Atlantic. Having made their eponymous first album, which included such classics as Stills’s “Suite: Judy Blue Eyes”, Nash’s “Marrakesh Express” and Crosby’s “Guinnevere”, they added Young in time for their first concerts, with appearances at both Woodstock and Altamont before they made their European debut at the Royal Albert Hall in January 1970, at which they were unsettled by the reserved response of the British audience. With Young, they had already recorded a second album, Déjà Vu, whose highlights included Nash’s terminally twee “Our House”, about his relationship with Mitchell; Crosby’s “Almost Cut My Hair”, a response to the shooting of Bobby Kennedy and the recent death of a girlfriend; and – sticking out a mile – the new recruit’s plaintive “Helpless”. But Stills was already telling a British journalist: “It started out as a really beautiful idea. We were full of enthusiasm and ideals. Now a lot of that feeling has gone between us.”

Thereafter, in Doggett’s words, it becomes “the tale of how four individuals battled to maintain their separate artistic identities when much of their audience simply wanted them to repeat the past”. Neither book flinches from dealing with the way, to put it simply, the peace and harmony given by marijuana were taken away by the paranoia of cocaine. From their descriptions of the protagonists’ relations with battalions of compliant young women, the hero is undoubtedly Mitchell, who emerged from relationships with Crosby and Nash as an independent figure, using what she had learnt as material for her own songs, which have generally worn rather better than theirs.

Of the two authors, Browne is the more likely to produce sentences such as: “Between snorts of cocaine, the trio rounded up a few other musicians …” He seems not to know what “unison” means, which is odd for a man writing a book about one of the world’s most famous vocal harmony groups, and has a regrettable fondness for telling us that people “reached out” to each other. But he does have the granular detail, including the White House face-off, which Doggett misses. Doggett is the better writer, however, and has the sense to deal with the last 45 years in a dozen pages, while Browne spends 230 pages labouring through the endlessly repetitive disintegration of all that bright promise, by the end of which the reader’s spirits are thoroughly lowered. Even the glistening harmonies, finely crafted songs and lovely playing of that first album are dulled by the litany of excess and its concomitant unhappiness. And it all seemed such fun at the time, at least from a safe distance.

• Crosby, Stills, Nash & Young: The Biography by Peter Doggett is published by Bodley Head (RRP £25). To order a copy go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £15, online orders only. Phone orders min p&p of £1.99. Crosby, Stills, Nash & Young: The Wild, Definitive Saga of Rock’s Greatest Supergroup by David Browne is published by Da Capo (RRP, £25).