Esko Männikkö lives and works in Oulu in northern Finland, and most of his photographs depict local people, animals, houses, things that catch his eye - whether it be the steps leading up to a clapboard house, a group of drunk Finnish men celebrating Christmas, or horses looking back at the camera. "I am a hunter," he says.  A few years ago, Männikkö, one of the four photographers featured in the current Deutsche Börse photography prize exhibition at the Photographers' Gallery in London, showed some of this work at White Cube. His richly coloured images are full of incident: sometimes a single detail, such as a spot of white on a horse's brown flank, or the skeleton of a pike; sometimes an entire roomful of things. He blows up and crops his images to fit the found or homemade wooden frames that he hangs in a wagon-train row, the frames abutting one another, along the wall.  Männikkö spends time with his subjects, getting to know them, waiting like a hunter to get the right shot. Unlike two of the other photographers in this exhibition, he takes no moral position, and says he is a "photographer of fish, dogs, and old men". This is overly modest, a disarming camouflage. One senses his work is far from done.  John Davies' photographs have been in my mind for a long time. His best known is probably a 1983 view of Agecroft Power Station in Salford. Photographed in black and white on a bright winter day, the four cooling towers of the coal-fired power station dominate the landscape. On the reclaimed land between the river and canal, two games of amateur football are being played. In the scrappy woodland beneath where Davies has set up his large-format camera, a few cars are parked, next to a scattered pile of fly-tipped rubbish. In the haze to the south looms the enclosed winding gear of the last surviving colliery in the Lancashire coalfield. (The pit closed in 1990, the power station three years later. It has now been demolished; a prison stands on the site today.) Davies's photographs keep you looking for a long time.  Time, in fact, is what they dwell on most. Davies' black-and-white work, with its slow, studied positioning and panoramic depth of field and focus, is a kind of social document. This, in any case, is a role that photography can hardly avoid. It is also true of the work of the three other photographers here - and for Jacob Holdt and Fazal Sheikh, social documentary is their declared aim. Holdt, a Dane, spent much of the 1970s hitchhiking his way across the US, befriending the people he met and letting chance and circumstance dictate his accidental travels; he called this "vagabonding".  After a while, Holdt began taking slide photographs of the people and places he went, and these images eventually became a book, American Pictures, as well as a slide show that Holdt has toured throughout the US and Europe ever since. Recently re-edited, and shorn of much of Holdt's deadly accompanying rhetoric, United States 1970-75 is not so much a series of images as an onslaught of several thousand slides, reduced here to 81, the number of transparencies that will fill a carousel.  There are prostitutes and playboy millionaires, junkies and swingers, Ku Klux Klansmen and former slaves. Transvestites, thieves, plantation ladies and Cuban maids, dead people, rednecks and racists, all jostling for our attention as the slides clunk through the projector. A small child peers inside a filthy refrigerator. A poor guy looks glumly into his coffee cup, as if he might find some important truth there. Holdt, too, was looking for something on his travels, and what he discovered was often deeply disturbing and unpalatable.  On his website, Holdt calls his corpus of images "a visually moving and therapeutically healing journey through the deep racist subconsciousness of the spectator". I think it is for us to decide what is moving or therapeutic, let alone how racist our subconsciousnesses may be. Watching Holdt's slideshow is frustrating. Nothing is on screen long enough to linger over. And as a photographer, Holdt is completely hit-and-miss. (He himself insists he is no artist.) At his best, Holdt is a magnet for the telling shot - whether it's a pair of guys turning to stare at him as they are looting a TV during a riot, or a spoilt girl smoking over her uneaten lobster at a Palm Beach dinner. But he lacks the ability to edit his own work, or to see what makes a striking or telling juxtaposition. He was a kind of innocent abroad, allowing himself to be led into the dangerous situations that enabled him to take the most compelling of his photographs. This indiscriminating attitude towards his work is also his weakness.  I have even deeper qualms regarding the photographs of Fazal Sheikh. In fact, I recoil from them. Sheikh, born in the US, lives in New York, Zürich and Kenya, and aims to be a sort of moral conscience, a witness to the worst the world has to offer. According to a writer in the Deutsche Börse catalogue, Sheikh has "transformed his practice from that of image-maker to social-change maker". I don't know what this means, or if any of it makes Sheikh a better or more interesting photographer.  Ladli is a series of black-and-white portraits of orphaned female babies, unhappy infants, teenagers and women. They face us and we face them back. Some are wary and anxious. Some turn their back on the camera (possibly at Sheikh's suggestion). Sheikh makes them all look beautiful. There are also photographs of clasped hands, a girl's suppurating leg (the leg has still not healed, two years after she was the victim of a hit-and-run), the rose petals that another girl sells on the street. The images are accompanied by extremely painful stories, which annotate the images and in which Sheik ruminates on social injustice.  All this is to direct our attention to the plight of women in India today. Which is all well and good, but I am uncomfortable with the tastefulness of Sheik's images, the coffee-table elegance of the book, the sentimentality of some of his accompanying texts. I am uncomfortable with his hand-wringing - not least because Sheikh has the hubris to group much of his work under the umbrella title The International Human Rights Series.  In the end, one has to ask who should win the Deutsche Börse prize, and it is Davies' photographs that won't leave me alone. They are dispassionate and compelling. In them, we see geology overlain with the social; the landscape quartered by roads and railways, viaducts and canals; back-to-back housing giving way to high-rise tower blocks that themselves are flattened. There is history in them, as well as light. They tell us things about cities and our relationship to the landscapes on which they are built, about human endeavour and folly. The slag heaps of the closed mines are forested; slate quarries become tourist attractions; trains wind between the houses on a Welsh hillside, carting containers of spent nuclear fuel. Racing pigeons wheel across a mild sky over Sheffield lofts that are about to be cleared for another round of urban expansion and renewal. There is no nostalgia here, only a kind of resignation. Neither Davies' photographs nor his accompanying commentaries tell you what to think or feel, for which I am hugely grateful. He deserves to win.  · Deutsche Börse Photography Prize 2008 is at the Photographers' Gallery, London (020-7831 1772), until April 6
Half the photographers up for the Deutsche Börse prize have a moral point to make. But it's the ones who don't, says Adrian Searle, that are the most interesting