Secret Policeman's Ball: Stand-up and be counted

London vs New York. Tube vs subway. Broadway vs West End. Get out of my way vs have a nice day. The rivalries between the two cities are long-standing and deeply felt. This week, The New York Times devoted an entire issue of its magazine to London, an honour somewhat undermined by its tongue-in-cheek characterisation of the city as a foggy, gin-soaked metropolis peopled by fun-hating, mealy-mouthed alcoholics and feral youths.

Which city, though, is funnier? Sunday night offered a chance to find out when both brought out their comedy heavyweights for the Secret Policeman's Ball. In the (sometimes really quite) blue corner, representing the United Kingdom, were Russell Brand (who scooped top billing amid no little competition), Jimmy Carr, Eddie Izzard, David Walliams, Catherine Tate and, umm, Richard Branson. In the red corner, representing the United States, were Jon Stewart, Ben Stiller, Sarah Silverman, Kristen Wiig, a couple of Muppets and most of the Saturday Night Live crew.

This wasn't simply a prize fight between stand-up superpowers, though. The Secret Policeman's Ball is a comedy night with a conscience and a purpose – to raise funds and awareness for Amnesty International. Who better, runs the reasoning, to stand up for freedom of speech than those who have made being outspoken an artform?

The Balls began life in 1976 when Amnesty noticed a certain J Cleese on its list of donors. Scenting an opportunity, it called the comedian up and asked him to gather a few friends for a benefit gig. His little black book yielded a dream line-up including Beyond the Fringe's Alan Bennett and Peter Cook, Dame Edna Everage, The Goodies and of course his fellow Pythons.

So it was that a sketch about a dead parrot – the opening act on that night at Her Majesty's Theatre 36 years ago – set in motion the now fully ingrained idea of artists lending their high profiles to good causes. Without the Secret Policeman's Ball there may never have been a Comic Relief or a Live Aid (Bono has said that watching one of the gigs "sowed a seed" in his mind). Since then, the poster bills for the regular benefits have featured a who's who of comedy talent. The last edition, in 2008 at the Royal Albert Hall, starred Tim Minchin, Sarah Millican and Kristen Schaal from Flight of the Conchords, among others.

This year, to mark the 50th anniversary of Amnesty International, the Ball left Britain for the first time in its history. And it's fair to say that the American connection ramped things up a notch. The venue was New York's Radio City Music Hall and the 6,000-strong audience (many of whom had paid $500 for a ticket) included Carey Mulligan, Harvey Weinstein, Evan Rachel Wood and Liam Neeson. So crammed was the bill that Wiig, Tate and Chris O'Dowd were among the stars buried with barely a couple of lines in multi-character sketches. Oh, and the house bands for the night were Mumford & Sons and Coldplay, who wrapped up the evening with their efficiently uplifting blend of singalong tunes, fluorescent paint and cannons firing paper butterfly confetti into the stalls.

The task of opening the event was entrusted, strangely enough, to Desmond Tutu, who got the night off to a good-natured start, assuring the audience via video that he was a "really, really funny guy". "People always say to me, 'Why don't you go into comedy instead of devoting your life to fighting injustice?'" he deadpanned admirably.

The joke was typical of a night which, in its scripted elements at least, toyed endlessly with the idea of whether comedy really can make a difference. With a writing team overseen by David Javerbaum of The Daily Show, it bore all the hallmarks of that satirical programme's searingly self-reflexive wit.

Most memorable among these sketches were Jon Stewart's awkward double act with "Kim Jong -un" (he had been expecting Kim Kardashian – cue some tricky knock-knock jokes) and Sarah Silverman's faux rallying call for human rights that skewered the solipsism of celebrity charity appeals and reduced the fight for freedom of speech to her customary self-lacerating trivial tales of dating and dieting woe. A routine from SNL regulars, Seth Meyers, Jason Sudeikis, Fred Armisen and Rashida Jones, which played out life under a dictatorship as a series of puerile point-scoring interrogation scenes was another highlight.

All of these sketches were admirably on-message and slickly delivered. On topical satire, then, the Americans won hands down. It was down to the Brits to deliver more in the way of lightly shambolic straight stand-up that for the most part studiously avoided politics or talking about the cause. Eddie Izzard and Jimmy Carr both trotted out tried-and-tested material proficiently, the former quickly abandoning American politics for a surreal deconstruction of Latin, the latter going for some bracing and quickfire smut to get the crowd on side before sucker-punching them with an al-Qa'ida-themed final gag.

Two relative newcomers – Micky Flanagan and Jack Whitehall – made the most of their big moment in the transatlantic spotlight. Coming straight after Mumford & Sons' clean-cut and heartfelt set (which was greeted with whoops and hollers by the crowd and with bashful bemusement by the band. "It's an awfully big place, this", mumbled Marcus Mumford), Whitehall capitalised on the Anglophile feeling in the room, bounding on to the stage in a neat little waistcoat, wide-eyed and plummy-voiced, like Hugh Grant's funnier, younger brother. In a near-perfect set, he presented his disarming take on new-fangled modern living from the pretensions of iPhones ("always jumping to conclusions...") to teenage sex and Tyra Banks.

The stand-out stand-up, though, was Russell Brand, and not only because he was "the only person performing who looks like he could have spent time in Guantanamo Bay". In the first of two sets, Brand – bearded, hollow-cheeked and with a rosary-style silver chain dangling dangerously from his crotch – riffed deliciously with his fellow raven-haired surrealist Noel Fielding on the subject of Amnesty membership. Having plucked a non-member from the audience they proceeded to rib her mercilessly – "This selfish cow of a woman! She's Hitler with a perm!" – using their brief to deliver some shocking Amnesty statistics and to "root out bigotry real quick", to spin off into strange little riffs on subjects including, improbably, stonings in Iran, to hilarious effect.

Brand re-emerged later for a solo set, which he devoted to eviscerating the media from Fox News ("I watched it for six hours and not one story about foxes... Misleading".) to MTV ("Like a pink pony trotting through our brains, shitting glitter"). He was the one unpredictable element in an otherwise smoothly controlled evening and all the more thrilling for it.

As for the US/UK rivalry, there were plenty of transatlantic collaborations that explored the theme, though these were generally the weakest elements. A sketch by Paul Rudd and Matt Berry played on the awkwardness of such showbiz marriages of convenience while David Walliams and Ben Stiller delivered a rather more traditional dissection of the idiosyncrasies English vs American vocabulary, the highlight of which was Stiller's crowd-pleasing reprisal of his Blue Steel pose from Zoolander. British comedian Peter Serafinowicz, meanwhile, was tasked with weaving Richard Branson and a series of well-known faces into a sketch about hacker-activists Anonymous.

So which city emerged the victor? If you like your comedy slick and satirical, New York edged it. If, though, you prefer the edgier ride of real stand-up, London won hands down with Brand the only comedian who succeeded in marrying mirth and message to truly original effect.

In the end, the evening belonged to neither Britain nor America. Introduced by Liam Neeson, it was Zarganar, the Burmese stand-up comedian who has been jailed four times, for a total of 11 years since 1988, who drew the night's only spontaneous ovation. On stage, he eschewed jokes and satire for a dignified reminder of the serious stories behind the evening's laughs. After the show, I asked Zarganar why he and his compatriots continued to tell jokes in the face of imprisonment or worse. "We can open people's eyes and people's ears and we can agitate and motivate," he said. "This is my duty for my people now."

'The Secret Policeman's Ball' screens on Friday at 10pm on Channel 4