Has the Turner Prize grown up?

There's no faeces, and remarkably little attention-seeking. Instead of the shock effects of years gone by, the 2013 exhibition that opened yesterday offers accomplished and thoughtful art, says Zoe Pilger

"How will you REACT?" The words greet the visitor to this year's Turner Prize, written on a poster, accompanied by a photograph of a stunned child. It hangs outside the former military barracks that have been transformed into a gallery space for the occasion, and comes into view as you walk across the Peace Bridge, over the river that once symbolically divided Derry-Londonderry, or just Legenderry, as the locals are proud of calling it.

The Turner Prize is perhaps most famous for trying – sometimes desperately – to elicit a reaction from its visitors. Last year, there was Paul Noble's sculptures of faeces and the ad-hoc performance art of Spartacus Chetwynd, renowned for living in a nudist colony.

This year's exhibition is better. It is more mature – perhaps with the exception of David Shrigley's installation – and less of a spectacle. Rather than attention-seeking zaniness, many of the works here are rooted in skill, craft, and subtlety.

From painting to film to installation to performance to a "constructed situation", the four shortlisted artists have created works that require thoughtfulness from the viewer, albeit in radically different ways. Too often, the Turner Prize is held up as proof that contemporary art really is a load of rubbish. This year, it proves the opposite: there is some exceptional art here.

This is the first time the prize has been held outside England, and Derry – as City of Culture 2013 – has done a fantastic job. Awarded every year to a British artist under 50 years old for an outstanding exhibition in the past 12 months, the prize money is £25,000. Each runner-up will receive £5,000.

The work that I love the most this year is Wantee (2013) by French-born Laure Prouvost, 35. The immersive film installation is based on the life of her fictional grandfather, supposedly a close friend of the German artist Kurt Schwhitters.

The viewer enters a dimly lit scruffily artistic dining room, complete with teapots shaped like cushiony bums and teacups painted with bright-red lipsticked mouths. There is a sense that the crockery could start talking to you, or trying to seduce you.

Indeed, Prouvost is a seductive artist. The film that accompanies the installation is sensual and difficult to fathom. Images of the aforementioned teacups are spliced with shots of the vividly green English countryside outside the window of the comfortably disarranged and tatty bohemian house in which her fictional grandfather, who was a conceptual artist, ostensibly lived.

Prouvost's breathy French voice-over is irresistible; so, too, is her poetic rambling narrative, her swerves into abstraction, her seeming joy in the medium of film itself. The work is enchanting without being fey.

How does she do it? I could easily hate all the components here: nostalgia, a fetish for pretty and ruined things. The film could be horrendously girly; it isn't. The narrative that Prouvost constructs is dark and strange, offsetting the sweetness. It transpires that her fictional grandfather created a "last concept" before he died: an escape hatch in the floor of the house. He began to tunnel one day, and never came back.

In a room to the right of the gallery, the bohemian mess has been replaced by chintz pink carpet and matching walls. The viewer can watch a video of Prouvost's fictional grandmother's dream, which includes an aeroplane that can pour tea from the sky, but focuses mainly on her wish for Prouvost's grandfather to love her forever. It is charming. The narrative is fragmented, but the meaning remains intact.

My second favourite series of works here is by London-based British Ghanaian artist Lynette Yiadom-Boakye, 35. These large oil paintings show imaginary figures in scenes that hint at narratives which are never revealed. Yiadom-Boakye paints from imagination, memory, and a range of sources, but the precision of each face points to characters who seem nuanced and real.

All her subjects are black. The colour of their skin poses a challenge to the history of classical Western portraiture, which Yiadom-Boakye draws upon. The paintings appear to be historical scenes of escape and survival. They show men hunting, dressing quickly in a forest clearing, staring confrontationally out of the canvas.

Perhaps most striking is Bound Over to Keep the Faith (2011), which shows a man in profile, smiling. His expression might be cavalier or humiliated. He is perhaps on the verge of manic laughter, but his eyes are sad. Or are they?

A thin rope snakes round his waist and he wears a shockingly white long-sleeved T-shirt, which is stark and abrasive and cold against the rich lushness of the dark brown background. Indeed, it is Yiadom-Boakye's skill as a painter that makes you want to look at her work for as long as possible. She has successfully brought back the outmoded genre of portraiture while making it knowing and aloof enough to satisfy the irony-mad conceptual art market.

Instead of paintings or sculptures, British-German artist Tino Sehgal's work consists of real people in matching black outfits, ranging from young to old, hanging around in an empty room. They greet me in a friendly and slightly cultish way, as though trying to convert me to some obscure cause.

One young man steps forward and informs me that he will give me £2 if I talk to him about the free-market economy. I say fine. He is very nice and good-looking. Our conversation becomes more flirtatious as we meander through subjects ranging from the welfare state and the mixed economy, to private education, and why communism might not be desirable.

I ask him how he knows so much about politics and he says he has degrees in history and international relations. The experience is fun and he is charming. I earn my £2, but then forget to claim it from the gift shop downstairs.

Sehgal, 37, is known for his "constructed situations", which star members of the public rather than actors. I'm not convinced by Sehgal; his work is minimalist, elusive, seemingly rooted in the ordinary occurrence of people talking to each other, but for me this points to a kind of arrogance. So we're talking about the market economy. So what? The exchange in itself is neither poignant nor banal.

Sehgal forbids documentation of his "situations"; his phenomenal success seems as much due to the mystery with which he surrounds himself as the content of the work. While Prouvost seduces by offering a visual superabundance, Sehgal withholds.

Perhaps the work most typical of Turner Prize puerility is David Shrigley's Life Model (2012), an installation which includes a giant, grotesque, malformed, naked figure in the centre of the room, surrounded on all sides by chairs and easels. There are crayons and pencils; visitors are encouraged to draw the figure, who has cartoonish blue eyes and large ears. His disproportionately small penis is pointed downwards into a bucket. Every so often, he pisses into it and blinks mechanically.

Shrigley, 45, is known for his dryly comic drawings. Different attempts at capturing the figure's hideousness already cover the gallery walls. Failure is inevitable in this peculiar, lurid life-drawing class. As Shrigley has pointed out, the figure is anatomically incorrect so even a perfect drawing will look wrong. Shrigley embraces the liberating potential of making mistakes. While I can appreciate the inclusiveness and fun of the work, it suggests a less well rendered Ron Mueck.

It would be a shame if Shrigley wins because this year's shortlisted artists seem unafraid for once of taking themselves and their art seriously, and, in turn, they ask the viewer to do the same. On the other hand, Sehgal's work takes itself a bit too seriously. Yiadom-Boakye is a wonderful painter, but I think Prouvost's delightful and generous story-telling would be a rightful winner.

Turner Prize 2013, Ebrington Barracks, Derry-Londonderry (turnerprize2013.org) to 5 January