SEPTEMBER 13th is the fiftieth anniversary of the release of “Yesterday” as a single: arguably the first solo Paul McCartney recording, and an early sign that he and John Lennon were drifting in different directions. It had come out a month earlier on the "Help!" album in America, but it was the first single release to feature the writing and recording of a single Beatle. As such, its anniversary makes an apt moment to ponder what made Lennon and McCartney's compositions so distinct, and why critics and journalists love pitting them against each other. A documentary film exploring the question was released last year, with 550 artists squabbling over “Lennon or McCartney”, just like the bickering voices in “Hello, Goodbye”: “You say high, I say low, / You say why, and I say I don't know”. (John won, 282 to 196, with a number of votes for the other bandmates and various other ineligible choices.) There’s even a split along political lines: a 2013 poll showed that Democrats pick Lennon as their favourite Beatle, whilst Republicans and independents skew strongly McCartney [see chart below]. The silver-haired are drawn to Paul's golden oldies; rebellious youths are drawn to John's revolutions.

Of course some fans vehemently defend George Harrison as the band’s most creative member, or prefer Ringo Starr’s understatement. Many baulk at the very idea of dividing up the Fab Four (again). But the rivalry and eventual animosity in the Lennon-McCartney axis makes comparing their contributions irresistible. Sir George Martin, "the Fifth Beatle" who produced the band's albums, likened it to "asking what's the most important constituent in a sauce vinaigrette, the oil or the vinegar?" Granted, the two substances go together brilliantly—but they separate naturally after a while.

Lennon and McCartney were rarely so diplomatic, and would have quickly decided which garnish referred to whom. Though they co-wrote many tunes "eyeball to eyeball" over a piano (Lennon's words), and brought others into the studio to "check 'em out against each other" (McCartney's), both men generally referred to songs as "mine" or "his". Not always in flattering terms, either. In August 1971 a McCartney single, "Too Many People", contained a veiled dig at Lennon and Yoko Ono's political invective: "Too many people preaching practices". Lennon's response in September, "How Do You Sleep?", was as blunt as it was swift. "The only thing you done was Yesterday, / And since you've gone you're just Another Day", he taunted, referencing two songs from before and after the split.

The rivalry had begun by the time the first Beatles' albums were released: "it wasn't resentment, but it was competitive," Lennon recalled. It intensified with the arrival of Ms Ono: "in the middle of the night [John] would say 'They always cover Paul's songs, they never cover mine.'" And it continues today, with McCartney occasionally grousing about the order of the iconic "Lennon-McCartney" songwriting. (He is legally powerless to change even his own solo compositions to "McCartney-Lennon".) At the lowest point of the relationship, in September 1971, Lennon told a painful anecdote on the Dick Cavett Show about a restaurant violinist playing "Yesterday" in his ear. The latter has since become the most covered song of all time.

Though it contains none of the acrimony that would mark the later recordings, "Yesterday", the song that Lennon spat back at McCartney after the split, is a good place to start when picking between the two. It was only released as a single in America; listeners in the UK had to make do with hearing it on Help!, as the band felt that a song which had been written and performed by only one member ought not to be promoted by itself. Featuring Paul on guitar, it was also the first Beatles recording to use classical instrumentation.

For those who prefer McCartney to Lennon, "Yesterday" is proof of what most would readily admit: Paul is the better composer, capable of producing complex melodies and arrangements that surpassed many of John’s brash, monotone efforts. The chord sequence for "Yesterday" came to McCartney in a dream, and was so flawless that as he scribbled it down at his piano, he was certain he had pinched it from elsewhere—an unfounded anxiety that Lennon prodded mischievously. While Mr Martin scored the first draft of the strings, McCartney was careful to add his own personal touches, subbing in various phrases for the cello and violins. His ability to tease out a memorable tune was nothing new, and continued into his solo career: "Band on the Run" and "Live and Let Die" had better hooks than anything Lennon came up with post-1970. Likewise, Paul’s penchant for dabbling in classical music has seen him release a number of orchestral albums, and produce a score for the New York City Ballet—a taste that first found expression in "Yesterday", followed by "She’s Leaving Home", and the triumphant climax of "A Day in the Life".

Fans of Lennon point to the latter song as evidence that John wrote the better lyrics. His musings on the death of Tara Browne, a friend killed in a car crash, are more profound than McCartney’s middle section about combing his hair and catching the bus; in turn, his lines about holes filling the Albert Hall are more perverse. Lennon’s later pieces veered from the pretentious ("Revolution 9") to the eccentric ("The Continuing Story of Bungalow Bill") to the daft ("Dig A Pony"), but they were rarely bland. Speaking of "Yesterday" in 1980, he carped that "if you read the whole song, it doesn’t say anything; you don’t know what happened." Lennon's finest lyrics, from "Working Class Hero" to "In My Life" to "Woman" to "Help!", have a purpose and a freshness of expression that McCartney rarely achieved. "My independence seems to vanish in the haze" trumps the clichéd "Suddenly, I’m not half the man I used to be." (For a long time, Paul's placeholder lyrics to "Yesterday" began "Scrambled eggs, / Oh my baby how I love your legs", which he gamely performed in 2013 with Jimmy Fallon, an American chat-show host.)

There are, as ever, exceptions. Paul’s "Eleanor Rigby", along with its sinister strings, has a morbid narrative that John would be proud of; Lennon’s "Because", inspired by Beethoven’s Moonlight sonata and requiring a nine-part harmony, could have been lifted from a McCartney scrapbook. At their best, both men crafted songs that few others are capable of. That they did so in tandem for so long should be enough to appease any fan.

Correction: An earlier version of this article referred to "The Continuing Adventures of Bungalow Bill", it is of course "The Continuing Story of Bungalow Bill".