The Warhol exhibition at the Barbican is all style and very little substance. But then art wasn't what he was best known for. He was famous simply for being famous.

Pretty soon, people will be asking some silly questions and getting back some awkward answers. Who, they will wonder, is Man of the Century? Adolf Hitler, obviously. And Artist of the Century? Well, it has to be Walt Disney, doesn't it? Pure fame is a great mocker, no encouragement to virtue or genius.

We know this. We know how, at the top end of artistic celebrity, results start getting funny. A few years ago there was a "most famous artist" poll, and the answer came out as Rolf Harris. Of course, this was a purely UK opinion, and I'm not sure whether it was a test for most famous living or most famous ever. Maybe Rolf came in only second or third. But the lesson stands. If you're looking to be an extremely famous artist, expect some bizarre competition.

And Andy Warhol knew this well. When his book The Philosophy of Andy Warhol came out in 1975, the blurb described him as "the most famous artist in the world". If that statement was doubtful, it wasn't so much due to potential rivals. (Picasso was dead, though Dali wasn't.) It was because by that stage Warhol was hardly a famous artist any more. He had diversified, and his various doings and appearances had become epiphenomena to the central phenomenon of Warhol. He was just plain famous.

There are two Warhol shows in London now. One treats him as an artist. At the Tate there's a small exhibition of pictures, some belonging to the gallery, some borrowed from the Froehlich Collection, which suggests, what Warhol shows tend to suggest, that as an artist he did some fine things from the late Fifties up to when he was nearly assassinated in 1968. The soup-tin paintings, the images of Marilyn's face and the electric chair: in these works Warhol's trademark blankness made a strong point, and it was a new point in art. Looking at them, you don't need to think of the Warhol phenomenon.

In the other show, that is exactly what you get. It's big. The Warhol Look: Glamour, Fashion, Style fills the whole of the Barbican Gallery. It is organised by the Andy Warhol Museum in Pittsburg, and doesn't include a lot of art. It dwells on the whole range of Warhol's interests and activities - commercial illustrator, window-dresser, screen-idol idolator, boho gang- leader, gossip-column filler, aspirant transvestite, movie maker, magazine owner, dedicated follower of fashion.

With another artist, you'd call it an exhibition of memorabilia, mere ancillary material. There are photos of Warhol hanging out with members of The Factory or with big-name designers; reconstructions of his shop- window displays; videos of his movies (which are really home movies); old copies of Interview, full of his wigs and toiletries; his own clothes; clothes inspired by his art; his collections of pictures of Marilyn Monroe; a pair of Clark Gable's shoes kindly given him by Gable's widow.

But with Warhol - so the show would like us to think - the concept of extra-artistic business doesn't really apply. Every bit of stuff counts. What we have is a life-project focused on fame and glamour. Fame was his obsession, his subject, his medium.

All that is true - and this is a much truer Warhol exhibition than any that just give you the art. At the same time, it's a show whose entire contents could be binned without any loss at all. At least, the only sort of visitor it's likely to satisfy is someone who has an obsessional interest in Warhol, who wants to know everything about him, is in fact as interested in Warhol as Warhol was in Marilyn and Liz Taylor, who desires Warhol's wigs as much as Warhol desired Gable's shoes. And there aren't likely to be many of them.

What went wrong? Was Warhol, the master of fame, still not quite famous enough? Well, Warhol wasn't the first artist to make fame an essential component of his work. The obvious precedent is Oscar Wilde. But it seems to me that a large exhibition of Wilde's bits and bobs could sustain interest in a way that the Warhol version can't, and that this has nothing to do with Wilde being a better artist. It's a matter, if you like, of superior fame-management, of having something to fall back on when the immediate blast of your fame begins, as it inevitably will, to fade. Wilde had a life and personality that shed interest on everything he touched. Warhol did not.

Of course, at the time that was a big selling-point, what made him a figure - his anti-personality, his hypnotic vacancy, his glazed expression and numb voice declaring that he was surface and nothing but. And this fitted with Warhol's general theory of fame - that it was a pure force, a mysterious, blank, irresistible influence with no psychological dimension. The theory works - but only in the short term. That is what fame feels like when its full heat is on. There's no arguing about why you're fascinated; you just are. That sort of fame Warhol could sustain. But, later, vacancy was bound to take its toll. The fame failed, and there was nothing to back it up.

And without the full, enveloping glare of Warhol's fame, the whole multi- part phenomenon begins to fall apart. The various enterprises become a series of disparate forays, none of them of much interest. The window displays: it's cruel to show them in an art gallery. The Factory: a futile bunch of wannabes. Interview: Hello! avant la lettre. Warhol himself: a pretty depressing individual, a man with an act that quickly wears thin. Everything stands exposed. And perhaps this is true to Warhol, too. Perhaps he knew well that the phenomenon wouldn't last, and never meant it to. If so, this self-imploding show is pretty conclusive proof.

'The Warhol Look: Glamour, Style, Fashion' is at the Barbican Art Gallery, London EC2, until 16 August (pounds 6, concessions pounds 4). The Warhol display is at the Tate Gallery, London SW1, until 20 September (admission free).