Don't get me wrong. 'Alvar Aalto through the eyes of Shigeru Ban' is definitely worth seeing. How could it not be? Aalto, one of the truly great architects, responsible for an almost untouchable legacy of fantastic, rewarding buildings. More than mere buildings, too. Responsible also for a body of thinking which ranges from the inherent properties of material itself right up to the point of building in the first place, and helping define the image of the modern architect. Oh, and furniture too. And then Shigeru Ban, one of the most consistently interesting architects today, with little formal connection to Aalto but a similarly thoughtful, responsible approach to architecture. Both architects represent ongoing attempts at connecting the vernacular, situated, and sustainable with the progressive, the innovative and the modern.

Yet the Barbican's exhibition is too withdrawn, recessive in presentation – a solid, unspectacular response, perhaps attempting to allow the numerous original drawings and models to breathe. It only really works the space in a pleasing central shelter of Ban's creation, cardboard tubing providing a canopy of waves over two undulating screens. While the explanatory exhibition displays do work aesthetically – lovely wall-mounted wooden boards, clean type with a dash of the Finnish aesthetic – they convey only brief biographical details. There's frustratingly little attempt to explore the work in real detail.

At one point, there is a beguiling note about how the Shigeru Ban Laboratory at Keio University has uncovered consistent formal patterns in Aalto's work. Apparently rejecting the 'simplistic application' of the golden section familiar in other modernist architecture, Aalto's architecture seemed to have an instinctive, organic flourish. Yet Ban's research seems to indicate recurring patterns, angles and geometric forms. After teasing us with this revelation, however, the exhibition presents an unlabelled image of the golden section 'in action', some unexplained overlays on Aalto's plans, and no more. Elsewhere, a virtuoso unfolding of possible forms for the MIT Baker House extends across the gallery, but with little explanation of the differences and why Aalto ended up at his conclusion.

As a punter, I'd like exhibitions to explain more. They exist to present a curated view of work, but also to explain this particular curation, and the significance of the work. I'd prefer them to be confident, unafraid of being didactic.  I'd like an exhibition to over-compensate, and let me decide when I'd had my fill. Spending £8 on the exhibition ($16 US; $20 Aus; €12; ¥1875), you should walk away full of ideas, inspiration and knowledge, without feeling you have to spend a further £30 on the catalogue.

However, the work itself, principally Aalto's, is of course wonderful, and I did walk away full of ideas, inspiration and knowledge (and with the catalogue). It's a greatest hits collection, curated by Ban, featuring mainly Nordic and Scandinavian projects, though also some outside of that territory, such as the Baker House dormitory at MIT, the Finland pavillion at the New York World Fair, and La Masion Carré nr. Paris. Aalto's extensive career in furniture, including entrepreneurship in creating the Artek firm, is well represented. There are numerous examples of Aalto's original sketches, and of the wondrous technical drawings and models of his firm. As a form of wordless explanation, simple white models by Shigeru Ban's students and practise do perform a valuable role in interrogating aspects of Aalto's work – as with the delightful models depicting the flooding of natural light through the giant skylights in Helsinki's academic bookshop, or in the Paimio Tuberculosis Sanatorium.

In an interesting move, entirely in keeping with his interests, Ban also includes Aalto's lesser known AA-System Houses, a form of prefab housing for the post-war period. A fascinating project, they rested on a tension between mass production and Aalto's beliefs in flexibility and in building to the highest quality for the greater part of society. Typically, he came up with his own theory of 'flexible standardisation', apparently influenced by organic structures – almost a precursor of biomimicry, perhaps, not the only way in which the AA-System Houses play to contemporary concerns.

This work also provides an effortless segue into the brief presentation of Ban's work in temporary housing after the Kobe earthquake and 2004 tsunami. Comprising no more than a few models, there's not enough here. Ban's work fusing paper tubing, vernacular forms and modernism is quite unique, and deserves more than the space he's given here, even in an exhibition primarily about someone else. The idea of getting Ban to curate Aalto is a brilliant one; yet this exhibition doesn't really deliver on its promise. Aalto's thinking and practise has influenced architecture from the Arctic Circle to Australia, and what could've been a fascinating exploration of this influence, with Ban as an example, actually comes down to around ten models, with brief explanatory nameplates. Although the models of his students also permeate the Aalto presentation, attempting to coax the work into speaking for itself, Ban has more to give.

The handsomely produced accompanying catalogue has more detail of course, and is worth getting, not least for Judith Turner's photographs. Capturing details of Aalto buildings in good light must be one of the easier, most pleasurable architectural photography assignments around, but she does it very well. The book also contains three selected essays by Aalto, a good long interview with Ban, an essay on Aalto's philosophy and design by Jahani Pallasmaa, a short piece by Colin St John Wilson, and all the text, photography and drawings from the exhibition.

As I said at the start: don't get me wrong, this is a very good exhibition, and do go to see if it you get the chance. But I fear it won't live as long in the memory as it should have done.

Below, after the links, you'll see I resumed my tense relationship with the Barbican's 'exhibition guards' by snapping a few surreptitious photos. Given the (ridiculous) subterfuge involved in taking these photos, the quality is fairly low. Still, I hope they give a sense of the exhibition. (Full set here).

Alvar Aalto through the eyes of Shigeru Ban, Barbican Art Gallery, 22 February 2007 – 13 May 2007, London
Exhibition catalogue: Amazon UK|US