Van Gogh's Letters: The Artist Speaks, Van Gogh Museum, AmsterdamThe Arts of Islam, Institut du Monde Arabe, Paris

Van Gogh was a prolific letter writer who illustrated his correspondence with sketches for fully-fledged pictures still to come

You'd imagine that an exhibition in Amsterdam of Van Gogh's letters and another in Paris of the Khalili Collection of Islamic art would have little in common, and you'd be right. The only tenuous connection I can think of is that Vincent's great-great-nephew, the film-maker Theo van Gogh, was murdered by a Muslim extremist in 2004, and that the Khalili exists in part to point out that barbarism and Islam do not go hand in hand. The other likeness between the shows is that both are diffuse, one in a bad way, the other good.

For the past 15 years, curators at the Van Gogh Museum have been editing the artist's huge correspondence, an outcome of this being what is probably the most important art publication of the century so far: Van Gogh – The Letters, in six glorious Thames & Hudson volumes. Vincent was a prolific writer, the clarity of his thought radically contradicting the view of him as a one-eared loon. What makes his letters particularly exciting, though, is that they are also works on paper, pages from a serial sketchbook on which Van Gogh tried out new ideas for paintings.

Thus, at random, the letter from St-Rémy-de-Provence of 2 September 1889 to his brother, also Theo. Written from the famous asylum, this is characteristically generous – Van Gogh defends Ernest Meissonier, a once fashionable pompier painter, from criticism by Monet, before going on to champion the even more outdated Karl Bodmer. What is particularly curious about the letter, though, is that it contains a sketch of what would become the canvas Field with a Ploughman, an inclusion which Van Gogh oddly neglects to mention.

This raises the intriguing question of the connection in his mind and art between word and image. Do Van Gogh's drawings illustrate his text or the other way about? And what is the relationship between letter-sketches and finished canvases, some of the latter known only from the evidence of the former? These are meaty issues, and the evidence for debating them lies in the Van Gogh Museum's peerless collection of correspondence and paintings. So it is a shame that Vincent's letters have simply been dotted around the collection, often with no readable translations or obvious link between paper and canvas.

The letters project and its six-volume result are astonishing things, but this show isn't edited with the same acuity. It is to be hoped that a smaller version, due at the Royal Academy in January, will be more focused.

By contrast, one of the many virtues of the Khalili Collection is its apparently wilful lack of focus. There is something of The Arabian Nights about it, both in terms of the collection's miraculous scope and quality – 20,000 objects spanning 1,200 years and a swathe of the world between Morocco and China – and in the fact that it has no home: like the treasure of some sharp-eyed djinn, its purpose is to travel and to amaze. More, says its creator, Nasser Khalili, the collection is intended to act as an ambassador for Islam. Given that Khalili was himself born into a family of Iraqi Jews – a population reduced since 1948 from more than 100,000 to fewer than 100 – this ambition seems less miraculous than saintly.

The other great strength of the collection is its founder's insistence that works be seen from an Islamic, rather than a Western, point of view. The current show has travelled to Paris from Abu Dhabi, where the audience, presumably, will have been markedly different in terms of cultural expectation. The exhibition at the Institut du Monde Arabe includes about 500 works – or 2 per cent of the Khalili Collection – described in its literature as "masterpieces".

Deciding which objects count as chefs-d'oeuvre is a highly charged process, open to accusations of cultural bias. Islamic connoisseurship involves a knowledge of the Koran and of Arabic calligraphy, interests which, if reflected in this show, would have resulted in far shorter queues to see it. At the same time, the purpose was clearly not to pack the institute's galleries with 16th arrondissement ladies eyeing up the jewellery. One of the triumphs of this exhibition, to my inexpert eye at least, is its balance of hard scholarship and beautiful things.

I'll admit, though, to having emerged from it puzzled as to the usefulness in the context of the term "Islamic art". To call a show spanning the entirety of the fine and decorative devotional and secular arts, made everywhere from Los Angeles to Vladivostock and from AD800 to now, "The Arts of Christianity" would quite properly raise eyebrows. So why Arts de l'Islam? Whatever. For all its cleverness and diplomacy, for all its size and scope, one way of enjoying this wonderful trove is as a gathering of exquisite, formal things: from the anachronistic modernity of a 12th-century Afghan glass jug to the illuminated poems of the 15th-century Persian mystic Jalal al-Din Rumi; from an Ana-tolian star-medallion carpet to a Nepalese turban crown. Prepare to be wowed, but to be wowed cleverly.

'Van Gogh's Letters': (00 31 20 570 5200) to 3 Jan 2010; ' The Arts of Islam' (00 33 1 40 51 38 38) to 14 Mar 2010