Polaroids: Mapplethorpe, Modern Art Oxford, Oxford<br/>Elizabeth Peyton, Whitechapel Gallery, London

In January 1973 the American artist Robert Mapplethorpe sent out the invitations to his first New York exhibition. Inside each black Tiffany envelope the 26-year-old enclosed a note giving details of the show together with a Polaroid photograph of himself.

He stands naked, face on, an instant camera clasped to his chest. Below the camera, a peel-off white sticker playfully covers his penis. The photo is bold and provocative, an image of a handsome young man already confident with his looks and talent.

The nature of the Polaroid process most readily lends itself to shooting spontaneous pictures, but what is so revealing about this photo – and the 90 or so others on show at Modern Art Oxford – is that Mapplethorpe considered their compositions so carefully, and clearly intended the results as finished artworks.

Right from the start, Mapplethorpe's theme was his friends and the Manhattan demi-monde they inhabited. During this period he lived in the Chelsea Hotel with rock singer Patti Smith, and her long, bovine face and big dark eyes stare out from several of the photos here. His other favourite subjects are himself, his boyfriends and the world of S&M gay sex. His camera lovingly records a naked man tied up in chains, as well as a close-up of leather underwear, unzipped, their contents about to tip out. When he is not photographing his lovers or the act itself (as in Charles and Jim Kissing, a semi-naked pair in a tangled embrace), he is alluding to sex, with suggestive still-life shots of an empty bed, its sheets drawn invitingly back, or a pair of hastily discarded cowboy boots and jeans.

Mapplethorpe, who died from Aids in 1989, is remembered as a photographer of celebrities. But, like Cecil Beaton, whose early pictures these often resemble – especially Nicky Waymouth, in which an androgynous beauty in pearls floats across the picture like a mermaid – this is because many of his friends later became famous rather than because he set out to photograph famous people.

The same can't be said of Elizabeth Peyton, a New York artist whose sole reason for being seems to be to make pictures of celebrities. Starting in the early 1990s, she began to paint small reproductions of photographs of famous people that appeared in newspapers and magazines. Her style is like fashion illustration, with bold strokes of colour to outline faces, rosebud mouths and bare white backgrounds for skin. Like Warhol, she is interested in celebrities whose lives have a dark side: Kurt with Cheeky Num-num shows Kurt Cobain with his kitten, while Pete is a watercolour study of Pete Doherty represented like an ecstatic Christ in a Mannerist altarpiece. Liam Gallagher appears here more than once, as does Sid Vicious.

Peyton's paintings have become extremely cool and expensive, the must- have artworks for the kind of people she depicts. You can see why they want them: her pictures are pretty as can be, their subjects always stylised to look more beautiful than they really are. No doubt some people see them as a kind of clever meta-art; hand-painted reproductions of iconic photos made in the digital age. But surely the reality is as shallow as the picture surface she paints.

While Mapplethorpe interpreted his world in gritty black and white, Peyton selects her subjects with hindsight and then glamorises them some more. Perhaps it says something about the way Britain and America have changed in the past 30 years that you come out of this show feeling like a child who has eaten too many sweets.