As British as sarcasm, Pet Shop Boys, at their best, deliver a music that is almost entirely digital and yet imbue it with a sense of humanity, making it hard to know how sincere they really are. Was "I've got the brains / You've got the looks / Let's make lots of money" an instruction or a critique? Does Chris Lowe actually do anything other than press 'Go' on his synthesiser and bang out a melody while selecting a hat from his favourite milliner? Does Neil Tennant actually take time crafting his lyrics, or do they simply get tossed out over a cup of lemon tea? Artifice or authenticity: that is the question.

On the evidence of this exclusive, unusually intimate performance, one can't help but wonder whether Pet Shop Boys themselves know the answer. During this short show at the renowned Hebbel Am Ufer Theatre in Berlin, they perform only eight songs – seven from their new album, Elysium, as well as an adequate cover of the 1968 Bee Gees track, 'I Started A Joke', a B-side to recent single, 'Winner' – and manage to veer awkwardly between the startlingly romantic and the painfully clumsy. This, as you'd expect, is indicative of the new album itself: it contains enough classic Pet Shop Boys moments to justify their continuing existence, and yet still slips up a number of times, forcing one to question whether they really have anything fresh to add. They have, after all, endured far longer than anyone might ever have expected back in 1984 when the first, pre-Stephen Hague version of 'West End Girls' failed even to merit a proper UK release.

Their arrival tonight is presaged by a triumphant hunting horn fanfare, tribal chanting, canned applause and boisterous hurrahs building to a fierce cacophony that sounds like a mash-up of a Japanese cartoon theme tune and a noise experiment conducted by Sonic Youth and Boyd Rice. It's at odds with a set that's sparsely decorated with six TV screens (to allow two vocal groups who join the Boys virtually for a handful of songs), one microphone stand stage centre and Chris Lowe's simple electronic set up to the right: a Korg, a computer screen and seemingly little else. The duo make a low key entrance, striding in discreetly from the wings, Tennant grinning “Welcome to Elysium" as Lowe pulls his fisherman's hat over his eyes, before a thunderous bass line kicks in – its weight the kind beloved by Berlin's young clubbers, none of whom are here – as 'Face Like That' gets underway.

The rush of affection that one feels for the duo at this point is undeniable. Even with such a basic set-up, and a lightshow that resembles little more than the iTunes Visualiser, Tennant and Lowe demand attention despite their understated presence. Their lack of movement on stage – Tennant occasionally strolling away from his microphone stand, often in the manner of a man welcoming pensioners to a bingo night – might at times seem uninspired, but at their stillest it's also redolent of Kraftwerk, the only other act to have negotiated a contract between the coldly dispassionate and the emotionally demonstrative.

It helps that 'Face Like That' is powerfully reminiscent of vintage Pet Shop Boys. Though it sounds like 1986's 'Love Comes Quickly' has been given a slightly gauche 21st Century makeover, its wit and style still manage to provoke a sense of nostalgia while reminding the select audience that the duo remain contemporary icons of electronic pop. 'Invisible', meanwhile, contains echoes of 'Rent', though there's also, believe it or not, something of M83's recent re-contextualisation of futuristic 80s synth-pop in the keyboard embellishments that reverberate through the song, and 'Leaving' offers further welcome familiarity: lines like “Our love is dead / But the dead are here to stay / They made us what we are / They're with us everyday" are delivered with a welcome English restraint that matches the song's economical arrangement.

At their heart lies an impressive balancing act: Tennant's deadpan delivery of sentimental lyrics, Lowe's aloof and yet tender musical constructions. These represent a classic display of British stiff upper lip, emotion communicated with the minimum of fuss, but what follows is less appealing. 'Winner', which Tennant reveals was written for Eurovision rather than the Olympics – “We're not afraid of being uncool," he pointedly confesses – is simply too pat, an electronic take on a formula adopted in recent years by Coldplay that's designed to provide a superficial sense of unity. There's room for stirring anthems in this world – Elbow's 'One Day Like This' being a case in point – but not when they're spelt out so obviously.

The same is true of 'Ego Music', a heavy-handed takedown of – you guessed it – musicians with egos, Tennant reciting examples of the kind of nonsense that we've read in a million interviews (“What can I tell you? I'm an artist, and of course I always had a humanitarian vision"). If it's satirical, it's no more so than The Sun, and Tennant ends up sounding almost as smug as those he's apparently lambasting. Fortunately, the night's revived by 'Memory Of The Future', in which the feel-good factor is presented in a slightly more delicate fashion, Tennant no longer signposting his coveted response thanks to a wonderfully succinct hookline – “It's taken me all of my life to find you" – that's almost as instantly catchy as the best they've written. 'Requiem In Denim And Leopardskin', written for a deceased friend, is also evocative of their better work, its affection for its subject encapsulated by the kind of lyrical detail for a glitzy demi-monde that Tennant has always demonstrated.

'Hold On', however, which punctuates the two, is surely a step too far even for the committed, the camp of their interpretation of Village People's 'Go West' magnified a thousand times, the sentiment so candied as to require a health warning, the lumpen arrangements seemingly stolen from a disco version of a Rodgers and Hammerstein Broadway musical (though in fact the main theme is borrowed from Handel). Low points like these highlight Pet Shop Boys' Achilles heel, the sound they make when they fail to tread the fine line between sentiment and schmaltz. Their love of theatrics is acceptable when it's presented as spectacle, but when it manifests itself in their music it smothers their finest quality, the peculiarly British articulation of matters of the heart. Their charm has always existed in their discretion and, though their more extravagant acts are at times satisfying, these threaten the finely tuned nature of their most affecting work.

The thing is, it's enough that Tennant projects his voice – which at times sounds so perfect tonight that its questionable whether even he is actually participating in the performance, and in truth occasionally sounds like he's taken a hit off a helium balloon – from behind a poker face. It's sufficient if Chris Lowe presses 'Go' and does little more than play one-fingered melodies on his keyboard. That Pet Shop Boys can often convey the loneliness of love, the pain of rejection or the injustice of modern day society with just the slightest of gestures and the subtlest of chord changes makes them precious. At their best they allow us to exercise a skill that we rarely get the opportunity to enjoy any more: our ability to read between the lines. It's neither their artifice nor their authenticity that makes them so valuable, but – accidental or otherwise – their occasional but still unique capacity for combining the two. They make the mundane mysterious.