Quite when the concept of coolness became a thing is uncertain, even to etymologists. As early as 1884, an academic paper noted the expression ‘Dat’s cool!’ among African-Americans. But it’s about 100 years since ‘cool’ entered the lexicon as an unambiguous description of something to aspire to (via jazz, inevitably), and it’s still a crucial concept in the world of pop: it’s being cool that meant the Strokes could attract 50,000 or so people to east London, even though most of those present were at primary school when the band released their two first two albums, which are the two on which their reputation rests, and songs from which comprised nearly half their set.

The Strokes shouldn’t be cool: they are the only major rock band to have two members who met at finishing school in Switzerland; they are the only major rock band built on generational wealth (the father of singer Julian Casablancas founded Elite Model Management and ushered in the age of supermodels). But cool they are. They are associated not with Swiss finishing schools, but with the Lower East Side of Manhattan, with grit and grime and the underground, with men wanting to be them and women wanting to have sex with them.

Nickel Creek, on the other hand, are very much not cool. Well, they might very well be cool in the world of ‘progressive bluegrass’ from which they hail, but this is a bit like marching into Aimé Leon Dore in the most stylish pair of red chinos from M&S and hoping for kudos. And whereas the Strokes gave every impression that they would rather be anywhere else but in London, with anyone else but each other, Nickel Creek bounded on to the Barbican’s stage, beaming and grinning and offering their thanks to the audience and each other with almost pathological frequency.

The Strokes were terrible. The sound was awful where I was standing (as it apparently was at a Paris show later the same weekend), and there were hordes of people leaving halfway through. Casablancas was incomprehensible between songs. As with the last time I saw them, one song was dropped from the setlist and replaced with a formless jam. It’s not that the playing was bad, just that absolutely nothing seemed to matter to them, with the possible exception of the cheque. I’ve been going to see the Strokes for more than 20 years, and this has been my reaction every time. So why do I keep going back? Well, first because the best of their songs – from those first two albums – are very, very good indeed, and I live in hope of hearing them delivered the way I want. But also because, fool that I am, I keep being drawn back by their absolute ineffable coolness. I kid myself with the notion that something that cool has to be good, at least once.

Nickel Creek were very much not terrible. All three of them sing wonderfully, and their playing is outstanding. The trio of siblings Sean (guitar) and Sara Watkins (violin) and Chris Thile (mandolin and assorted related instruments) first began the group as child prodigies; they’re in their forties now, and could probably knock you out a competent bluegrass rendition of anything from Monteverdi to Mingus. Their version of bluegrass is at this point a long way removed from Bill Monroe and the Bluegrass Boys – there was very little high-speed fingerpicking in their set – and at times it was more reminiscent of the lighter end of alternative rock reimagined for traditional instruments (‘Somebody More Like You’ sounded almost exactly like an amazing Squeeze single from 1981). Their harmonies, too, were perfect: on ‘Helena’, the three voices (and that of touring bass player Jeff Picker) thrill in those high, vibratoless, keening Appalachian lines.

But – and again, fool that I am – the lack of coolness kept putting me off. It shouldn’t matter – and goodness knows I’d have been furious had Thile replicated Casablancas’s attitude – but it was a little like watching three 1970s Blue Peter presenters at work in its complete wholesomeness. That’s not their fault, it’s mine. They are who they are, and they should continue to be so – and since they’re probably the most popular bluegrass group at work, they know what they’re doing.

But if both they and the Strokes were in town on the same night, I’d still go to see the Strokes. Because I’m an idiot.