Emerging from the mud of Ground Zero in New York City, and now very visible above the hoardings, the rusty steel skeleton of Santiago Calatrava’s new transport hub evokes the fossilised carcase of a dinosaur. It works well as a symbol for a construction project that seems to be progressing at an almost paleontological pace.

Twelve years after 9/11 only the Memorial Site is finished, and even the drama of that is still emasculated by the oppressive entrance through airport-style security and a long walk snaking through the construction site.

Calatrava’s emerging monster is the crown of a massive rebuilding of the city at subterranean level. The first small concourse has just opened and, elegant and white as it might be, it gives no hint of the scale or complexity of this eye-wateringly expensive transit hub. Projected a decade ago to cost $2bn (and to finish in 2009), it is now up to $4bn (and might be completed in 2015).

Calatrava has absorbed much abuse from a city that cannot understand how a station could cost so much – but this reaction does not perhaps take into account that the site stands on landfill and above the rickety remains of centuries of timber wharves and piers. The Hudson River wants to take it back and in the surge of Hurricane Sandy it did just that, causing hundreds of millions of dollars’ worth of damage.

The Spanish architect’s notoriously expensive and complex designs may sometimes deserve the criticisms they attract but here, in New York, I think he may have hit on something which will begin to define a new sense of public space on this traumatised site. Stations need a touch of ambition and complexity. The Roman scale of Grand Central makes it one of the city’s most loved landmarks, and the old Penn Station (inspired by the Baths at Caracalla) is still mourned half a century after it was demolished.

The skeletal structure of Calatrava’s roof, designed, in a banal cliché, to resemble the wings of a dove (and originally intended to be kinetic), is part-Gaudí, part sci-fi alien rib cage and part self-indulgent sculpture. But it also evokes the great 19th-century iron-and-glass termini, dramatising the concourse. Increasingly, more hinges on its success as it becomes clear that the other structures on the site are failing to create the drama necessary to counter the filmic tragedy of 9/11, its terrible impact seared into our memories.

There are, of course, commercial as well as civic and memorial imperatives: Calatrava’s concourse will be the gateway to a huge retail complex that drives most of the scheme.

From the first furious arguments about how Ground Zero should be rebuilt, it was clear that work here, at the west’s most emotionally charged construction site, was never going to be easy. It still constitutes a void at the heart of downtown, but its borders and its skyline are beginning to be defined and it is possible to start

judging what the welter of decisions made by myriad organisations and interests are likely to produce.

Construction work continues on Calatrava’s ‘ribcage’ roof in the shadow of the 1,776ft-high 1WTC tower

The most prominent building has proved the most disappointing. What was once dubbed “Freedom Tower”, but is now known more prosaically as 1WTC, was intended to be the centrepiece of Daniel Libeskind’s master plan. The architect – Polish-born, but born-again New Yorker – spoke sentimentally of the impact of the Statue of Liberty as he arrived by boat in the city as a teenager. His tower was meant as an homage to the torch-bearing form, twisting and torquing to a spire (a symbolic 1,776ft tall) and emulating the beacon held aloft.

Architects love metaphors of movement – despite architecture’s necessary stasis – and Libeskind’s plan of a cluster of towers swirling in a vortex was a classic rhetoric of architectural restlessness. The site’s developer, Larry Silverstein (who had bought the World Trade Center only a couple of months before 9/11), judged Libeskind too inexperienced and instead brought in his favourite designer, David Childs of corporate giants SOM.

The result is dreadful. Libeskind’s notion of an expressionistic, spiky tower may have been impractical but it at least embodied an idea. At the end of last year the new tower scraped through the vetting process of the Council on Tall Buildings to become recognised as the tallest building in the western hemisphere (a record formerly held by Chicago’s Willis Tower). It reached the record through its spurious “spire”, the last remnant of Libeskind’s vision, once a reference to Liberty’s torch but now merely an appendage atop a dumb chamfered block. With its clunky concrete base (a precaution required by the NYPD against future attack) and a form which refuses to relate to anything around it, the tower is a poor successor to the 1931 Empire State Building (which had become the city’s tallest building again after 9/11), a skyscraper whose spire seems a natural culmination of its stepped form, a style imposed by the city’s strict setback regulations.

Meanwhile, Rogers Stirk Harbour & Partners’ 3WTC is emerging from the ground, and Foster & Partners’ 2WTC (“the Kissing Towers”) remains a hole. The on-site museum, an oddly insignificant, sub-crystalline glass building by Norwegian architects Snøhetta, also looks as if it may disappoint. The news, however, is not all bad. In the midst of controversy over the height, cost and time overruns of 1WTC, Japanese architect Fumihiko Maki has completed 4WTC, a 72-storey, 977ft tower facing the memorial park. Based on a parallelogram plan and with a subtle, angled setback towards its top, it is a self-effacing, elegant tower. Its façade is so perfectly detailed that it appears to fade into the sky, not through garish mirrored glass but merely through the delicacy of its glazing.

In material quality, detail and modesty it is everything that 1WTC is not, an elegant structure that begins to weave the site back into the city.

Silverstein’s decision to rebuild the site as a purely commercial development went against the grain of a downtown area that is rapidly being turned into a top-end investment residential zone – the older buildings have proved easier to adapt as apartments than as contemporary offices. The developer was criticised as he ploughed on with plans in the wake of 9/11: many New Yorkers and victims’ families expressed their outrage, some suggesting that instead the whole site should be turned into a memorial park.

The on-site museum by Snøhetta

In such a context, young local architect Michael Arad has achieved something remarkable in his memorial design. The black, gaping voids of the Twin Towers’ footprints reflect a little of Libeskind’s notion of leaving the holes as scars, open wounds revealing the mud, slurry and twisted steelwork of the exposed foundations. Abstracting the idea through stone and water they have managed to satisfy the urge to remember and at the same time allowed the site – and the city – to move on. They also suggest that this is a site where the best architecture may all be below ground.

In the best New York tradition, Silverstein ignored public sentiment and ploughed on with his redevelopment plans. But, arguably, this is saving the site from becoming another upmarket, unlived-in residential enclave, the type of development that kills the city centre stone dead. It is intriguing that many office floors designed for big finance are instead being taken by media companies as finance moves to Midtown.

If the ultimate gesture of defiance is that the city should carry on as before, the new World Trade Center has achieved it. The redevelopment embodies an archetypically New York cocktail of loud protest, commercial interest, community resentment, political grandstanding and architectural compromise. But it is happening. The best of the plan is the way the new buildings are being knitted back into the city with new public spaces, roads and the continuation of Greenwich Street, which were stymied by the Twin Towers’ dumb anti-urbanism. Minoru Yamasaki, the Twin Towers’ architect, wrote at their inauguration in 1973 that “the World Trade Center is a living symbol of man’s dedication to world peace . . . a representation of man’s belief in humanity”.

That turned out to be a tragic irony. Perhaps, since then, a sense of cynicism (or realism) has settled into architecture. If New York manages to reclaim a piece of its city as true public space, rather than making do with the leftovers of corporate gigantism, that alone will be an achievement.