Damien Hirst: Two Weeks One Summer, White Cube Bermondsey, London; Tracey Emin: She Lay Down Deep Beneath the Sea, Turner Contemporary, Margate

The sharks are circling Damien while Tracey displays a quiet maturity in her latest work

Here, by the door, is Brown Jug of Water with Scissors, one of 35 paintings in a show by Damien Hirst. That is not paintings as in spots but paintings as in still lifes, or sort of. After the richly deserved mauling Hirst's last canvases received, sheer perversity makes you want to like these new ones, or at least to annoy people by affecting to. But as Brown Jug quickly proves, it cannot be done.

Let's be fair. When you walk into the echoing room in which Hirst's new paintings hang, the impression is of prettiness. The concrete floor, waxed to an expensive gloss, reflects the nearly three dozen pictures, most of which include sprigs of blossom. Some paintings are biggish, some smallish, some hung alone and others in series. For a moment, there seems to be a rhythm, maybe even a painterly intelligence. Then you look again and see that Hirst is a set designer, not a painter.

Up close, Brown Jug of Water with Scissors seems oddly old-fashioned, like a Ben Nicholson post-Alfred Wallis. The difference is that Nicholson painted badly on purpose; Hirst doesn't. Nicholson's work was good-bad, Hirst's ... well.

Like Alice's bottle, these new canvases should be labelled "Deconstruct Me". Their ill-assembled and badly painted parts pick out the history of Modernist painting, from Cézanne's lemons via Picasso's guitars to Francis Bacon's box-spaces. At the end of this distinguished line is a new set of symbols – sharks' jaws, butterflies, deformed babies in bottles. And which Britartist has made butterflies, sharks and pickling under glass his trademark? Hirst's chutzpah is almost beguiling, but not quite.

And so to Margate, and something wonderful. I think it is fair to describe Tracey Emin's art to date as a protracted emotional explosion, a self-portrait whose disparate parts – monoprints, stitching, neon tubes, beach huts, beds, etc – echo the fragmenting of her own life. Now the force of Emin's art has reversed itself, from centrifugal to centripetal, from explosive to implosive. All those far-flung bits have suddenly come together, and in Margate. Emin has come home.

Happily, the only parallel I can find with Hirst's so-called rediscovery of paint is that Emin, too, is exploring art history. Unlike Hirst, though, this is not to big herself up: rather, it is to take back what is rightfully hers.

If men have been a problem to Emin as lovers and abusers, then they have been a pain as artists as well. It was a male painter, Gustave Courbet, who painted what remains the most famous image of a woman's genitals, L'Origine du monde. Rodin also had a go: in a small, in-between gallery, Emin has hung his Courbet-ish watercolour, Femme nue assise aux jambes écartées (Nude woman with legs apart). By way of riposte, she has produced Thank You – a large portrait of what I assume to be her own genitals, an image deeply feminine in being a tapestry and yet perversely masculine in depicting what is, after all, the defining anatomical characteristic of womanhood.

What is moving about Emin's show, She Lay Down Deep Beneath the Sea, is its sense of resolution, the way that parts of her art that have until now seemed disjointed and sporadic suddenly come together. In the Turner Contemporary's West Gallery are a series of gouache drawings. If Hirst can't paint, Emin certainly can draw: the series that includes the blue-on-blue Reading My Thoughts has the assurance of Matisse.

Diagonally opposite these are word works, inscribed with those trademark Eminisms which I have previously found annoying. Seen here, you realise that image and word have always been trying to get back together in Emin's art, the words to be graphic, the images calligraphic. Finally, at home in Margate, they are reunited.

It is risky to look to Emin's own life for an explanation of why this can happen now, why here. And yet, more than any other artist I can think of, her art calls out for biography. In the South Gallery are works in which she takes on that most inescapably male of artists, Picasso. (Or, as Emin spells him, "Picaso". Just stop it, Tracey: it's silly.) In Shadow Image, a Picasso-esque woman's face is sewn on to calico, the cruciform seams that hold the work's panels together like the cross threads on the site of a gun. Taking back power as a woman is a painful business, and a dangerous one: in the end, it may mean dispensing with men altogether. On the gallery floor is a small cat modelled in white patinated bronze. Emin has called it Real Love.

Mad Tracey, a spinster with cats? Why not? In the show's last room is a wooden obelisk, on which, set too high to see, is another small, white patinated bronze. This one is called Self Portrait with My Eyes Closed. The plinth looks like Emin's infamous beach hut, recycled 12 years on into something modestly triumphant. Nearing 50, Emin can finally make a monument to herself, even if it is a frail one. I'm glad.

Damien Hirst (020-7930 5373) to 8 Jul. Tracey Emin (01843 233000) to 23 Sep

Critic's Choice

Defy gender stereotypes and pop into both the V&A's fashion gallery and The Wallace Collection. Ballgowns: British Glamour since 1950 is at the V&A – marvel at the skill behind these fantastical garments. Or – en garde! – at the latter, The Noble Art of the Sword reveals the history of the sport of sword fighting, and the art of making Renaissance rapiers.

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