Pablo Picasso and Francis Alÿs

More Picasso. More achievement. More genius. More doubts.

A few weeks after the opening of Tate Liverpool’s ambitious exploration of the artist’s intense relationship with communism, the world’s most powerful private art gallery, the Gagosian, has unleashed an alternative view upon us withPicasso: The Mediterranean Years, 1945-1962, a mixed show of paintings, sculptures and ceramics, curated jointly by Picasso’s brilliant biographer, John Richardson, and the artist’s intriguing grandson, Bernard Ruiz-Picasso.

The Gagosian show covers more or less the same era as Liverpool’s: Picasso’s post-war years. But all similarities end there. In every other respect, we might as well be dealing with another artist, another human being.

Picasso’s move to the south of France at the end of the second world war certainly marked a new phase in his life. The war was over. The sun was on his back. He had a new girl in his bed, the enticingly young Francoise Gilot, who gave him a new family, naughty Claude and enchanting Paloma, both of whom figure delightfully here in Picasso’s most scampish and vivid child art. He was also closer to his beloved Spain than he had been since he had left her, half a century before, and the timeless magic of the Mediterranean had begun to work on him like a fine old wine, filling his dreams with intense Ovidian yearnings and insistent memories of ancient gods.

It is an exceptionally rich context. Yet the art it encouraged, the art in this show, has about it an uncomplicated air of pure release. A prison spell is over. A criminal is free.

The first thing you see is a girl in a bikini. Or, rather, a voluptuous terracotta pot onto which Picasso has slyly painted a skimpy yellow bikini. Most of us gazing at unpainted terracotta see only a dusty brown. Picasso recognises the exact tonality of the perfect Riviera tan. It’s a one-line gag, but a brilliant one, and here it sets the mood instantly, transporting us so effortlessly into the world of Brigitte Bardot and St Tropez, witty seaside flirtation and naughty peepings on the beach. Because this is Picasso, and because there is always more going on in him than in others, you sense, too, a deeper Mediterranean understanding smuggled through in these deceptively slight celebrations of the present. Even the bikini vase, as you stare at it, begins to acquire a mythic presence. This is not just a monument to some casual Sylvie encountered on the beach. This is a monument to the ancient Venus residing inside every casual Sylvie.

Basically chronological, the show is divided into compatible clusters. The earliest work, created just after the war ended, has a transitional air to it. Mostly grey in tone, it records the arrival in Picasso’s life of Gilot, a 24-year-old lover with whose image he never quite arrives at closure. First he paints her as a human flower. Then she becomes a gothic stained-glass window. Finally, in a brilliant exhibit discovered in some little-known corner of the collecting world, she’s a woman with her hands in her pockets, painted onto a real door. With her big hair and big breasts, Gilot is always recognisable, even in Picasso’s most cryptic portrayals, but she seems never to have stamped her identity on his output in the way other mistresses had.

All such uncertainties cease, however, when she begins giving him children and he begins recording them. In particular, the sculpture of the period feels as if it records a powerful trade-off in spirit between Picasso and his offspring. They give him their energy; he shows them his magic tricks. The famous likeness of Paloma skipping, created so miraculously from cardboard and old baskets, achieves a sculptural impossibility by capturing the happy little girl bouncing in midair.

Among the paintings, those featuring Claude stand out, with their impeccable painterly understanding of a child’s mood. Is there, in the whole of art, a more vivid encapsulation of a little boy’s devilishness than El Bobo, the portrait of a grinning Claude holding up two fried eggs that rhyme, so naughtily and so Picasso-ishly, with his testes?

In the past, Picasso’s long residency on the Co´te d’Azur has been understood as a period of decadence and loosening. That was how the celebrated Marxist art critic John Berger presented it in his bitter attacks on the artist. Richardson and Ruiz-Picasso’s version of these same years understands them instead as a period of intense Mediterranean renewal. The Picasso presented here is a sun-loving, girl-loving, bull-loving, food-loving and family-loving magician, with quicker hands than any dutiful communist ever had.

At the centre of the show is a nocturnal cabinet filled with largely unfamiliar sculptures, dramatically spotlit to intensify their voodoo effect.

The hey-presto baboon, made from two of Claude’s toy cars, is here, as well as a haunting cross, called Homme, which reduces the human shape to a harsh Golgothan vertical traversed by a harsh Golgothan horizontal. It’s such a familiar shape.

Yet Picasso has somehow recognised a brutal hopelessness in it that everyone else, in all those centuries, had missed.

This emphasis on his voodoo powers in the dark cabinet of fetishes is a typical Richardson gloss. His Picasso is always out to effect supernatural changes with his art, or lance ectoplasmic boils.

While Richardson brings his typically orgiastic understanding of Picasso to the event — I was disturbed by suggestions in the catalogue that Picasso’s relationship with his daughter Maya was incestuous — Ruiz-Picasso has made excellent use of his address book and filled the show with little-seen items from the family collection. They give it an unusually intimate air, as if we have been granted access to a family scrapbook.

Picasso’s final mistress, Jacqueline, whom he was eventually to marry, quickly becomes an insistent presence in his work. She, too, has big boobs and big hair, but it is the queenly air he gives her, as if her rightful place is to be enthroned at the centre of his art, that becomes her chief distinguishing characteristic in a superb concluding room. These are thrilling sights, impeccably installed along a clever route. So good is the show, many will feel tempted to recognise this Picasso as the real one and to assume that the good communist who turns up so dutifully at those Soviet conferences in Liverpool must have been some kind of doppelganger or evil twin. But to believe the Gagosian Picasso above the Liverpool one would also be a mistake. The only final truth about Picasso is that there is a version of him available for everyone.

At Tate Modern, in a contrast so vivid, the Fates themselves must have arranged it, the Belgian artist Francis Alÿs has somehow constructed a Tate-sized career for himself by making and remaking the same work. It consists of someone or something doing something hopeless on film, again and again. A VW Beetle keeps trying to mount an impossibly steep road. A boy kicks a bottle up an impossibly steep hill. Five hundred volunteers with shovels attempt to move the sand on an impossibly steep dune.

In all these cases, Alÿs is searching for a poetic metaphor to describe the unrewarding nature of modern labour, the repetitive and seemingly endless lot of the modern worker. On their own, all these pieces probably have a perfectly valid impact. I know, because I have encountered several of them before. What they certainly do not lend themselves to is the presentation of all of them at once, one after the other, in a line.

If ever an artist deserved better than to be given a retrospective at Tate Modern, it was Francis Alÿs.