There is a band of buildings, skilful and brave in their design, that will feature prominently in future histories of current architecture. Some are world famous, some are hugely popular, some represent new ideas surfacing for the first time. All share the same badge of honour. They did not win the £20,000 Riba Stirling prize, the award for "the architects of the building which has made the greatest contribution to British architecture in the past year".

These buildings include the Eden Project in Cornwall, Tate Modern, Selfridges in Birmingham, the New Art Gallery in Walsall, Will Alsop's Hotel du Department in Marseille, Zaha Hadid's Phaeno Science Centre in Wolfsburg and her BMW Central Building in Leipzig. The British Library in St Pancras, London, should also have won: although unfashionable and controversial when it opened, its quality becomes more apparent with each passing year.

Meanwhile the prize has been awarded to projects that have since subsided into obscurity. These include the Magna Centre in Rotherham, whose victory in 2001 seemed to surprise even its architect, Chris Wilkinson. The prize has an instinct for the compromise candidate, for the one least likely to frighten any horses.

This year some exceptional buildings haven't even made the shortlist, announced last week. One is the Nottingham Contemporary Art Centre by Caruso St John, a building that responds professionally to a demanding brief, budget and site. It is the work of client and architects who are both good and committed. Its galleries are scrupulously designed for the display of art. It deals beautifully with sloping terrain, allowing internal and external public routes to run through it. More than that, it tries something unusual, which is to see how ornament can be used on a modern building. It is clad in pale green concrete panels imprinted with lace patterns, creating a play of apparent lightness and actual heaviness.

Idea is translated into material, which is something architects should do. Nottingham Contemporary stands outside the usual run of decent-but-predictable modern architecture of which there is plenty. It is a public, civic building that makes a contribution to its city. It is an opportunity to recognise buildings north of Watford, which is something Stirling juries sometimes worry about, but the opportunity was not taken.

The list also omits the British Embassy in Warsaw by Tony Fretton, who must wonder what he has done to upset the Stirling fairy. Last year Fretton was the victim of a bizarre and nasty press campaign, which complained that two of the five prize judges were predisposed in his favour. This overlooked the fact that the other three weren't, or that, year after year, the Stirling jury is loaded in favour of the established and middlebrow.

As it turned out, the supposedly biased jury didn't choose Fretton's shortlisted entry, the Fuglsang art museum in Denmark. Instead they opted for Maggie's Cancer Caring Centre in Hammersmith, London, by Richard Rogers's practice, Rogers Stirk Harbour. This is a nice building, but it wasn't pushing any boundaries to reward a small project by a 76-year-old already amply recognised.

Fretton is not an ingratiating architect. His plain buildings can look ordinary in photographs. Nor is he a slick minimalist. What's good about his work is the subtle relationships he creates between building, people, landscape and – when they are galleries – art. It is surely part of the job of prizes like the Stirling to draw attention to the un-obvious, the things whose qualities are easily overlooked.

Rather than Nottingham and Warsaw, the shortlist this year's prize includes two schools, and a house and studio built by an architect couple for themselves. All are good buildings, designed by lovely people, and it's possible that the jury wanted to send a message to the government by including the schools. Look, they seem to be saying to the school-axing Michael Gove, the design of places of learning does matter. But the house doesn't open up new ideas the way Nottingham does, or have its public importance, while the prize's role is to recognise the best architecture rather than send messages.

Also on the shortlist is the extended Ashmolean museum, Oxford, by Rick Mather Architects. This earns its place for the way it organises a complex array of galleries behind the museum's original, Grade I-listed building. But it displays a cloth ear for materials, structure and detail. Its glass and steel balustrades are in jarring shopping-mall moderne, and if the choice was between this and Nottingham, the latter should have won.

The good thing about this year's list is that it includes the two projects that were always the most likely and deserving winners, Zaha Hadid's MAXXI (Museum of 21st Century Arts) in Rome, and the Neues museum in Berlin by David Chipperfield with Julian Harrap. The latter is a beautifully poised, meticulous, but also creative shaping of a new museum out of the bombed-out ruin of an old one. It is a smash hit in its home city. It represents a way of doing architecture, where the signature of the architect is not always apparent, that breaks with the icon-building of recent years.

MAXXI is a Wagnerian blast from the brass section of the orchestra. It is the consummation of years of imagining and fighting for new ways of forming and arranging buildings. It has flaws, but it is a magnificent urban experience, a passeggiata played out on multiple intersecting levels. Hadid, the most famous woman architect in history, and possibly the most famous living British architect, has never been recognised by the Stirling. In Stirling-think, this would be a reason for giving her the prize.

To choose between these two is tough – Berlin just shades it for me – but if either wins the Stirling will break its habit of shirking the most powerful works. The thing to fear would be a split jury when the winner is chosen in October, with a third, compromise candidate surging through. Then the Stirling really would have lost all claim to be about the best architecture, as opposed to the smooth management of judging committees.