I am staring in quiet desperation at the welter of statistics and oh-so-atmospheric videos and slightly feeble art installations to be found in Tate Modern’s Global Cities exhibition. I’m thinking of doing a runner before I die of boredom. No doubt this shows on my face, because a Tate Mod PR person homes in on me. “As you see,” she purrs, focusing my gaze with a flick of her elegant fingers, “we have Frank Gehry here.”

And yes, there is the little guy who hit stardom with the Bilbao Guggenheim, being escorted round. I’m fond of Gehry, but no, I don’t want to talk to him right now. No offence. Oh, blimey, there’s Zaha Hadid, too. Look, she’s great, but I really must dash. There are days when I just don’t much fancy the big business of world architecture.

Luckily, I am saved – and so is the show – by the architect and mischief-maker Nigel Coates. His Mixtacity installation, a wild, allusive, collagist vision of what the Thames Gateway might become, is funny, wise and beautiful. Coates has built a few interesting things in his time (remember the Body Zone in the Dome?), is professor of architecture at the Royal College of Art and is a bit of a living legend, frankly, but he’s not a global meganame in the sense that every city in the world thinks it has to have one of his buildings. Therefore, I want to talk to him. In fact, the words I greet him with are: “Thank God you’re here.”

In return, Coates shows me his model estuary townscape made of biscuits, sugar lumps, cotton bobbins, tacky souvenirs, replica guns and giant human hands. Nobody is ever going to build this stuff. Nor is that the idea. But it all seems remarkably plausible, like what goes on inside a Jake and Dinos Chapman vitrine. Somehow it means more to me, at this private view, than the real-life projects of Gehry and Hadid, Rem Koolhaas, Daniel Libeskind, Jean Nouvel, Norman Foster, Renzo Piano and the rest. And a lot more than Tate Mod’s comparative density diagrams of Mumbai and Cairo, which we’re meant to find so significant. What’s come over me?

I’m finding something oppressive about internationalist architecture, and how it is addressed. It’s done in two ways: the statistic-heavy, Google Earthy approach of Global Cities – the witchcraft symbols of the dominant urbanist sect – or the icon-building, signature-architect approach of just about every other show. Into this category comes the new biggie at the Design Museum, which might as well be called Zaha Superstar, since she has been given about three-quarters of the museum.

Now, Hadid is undoubtedly a superstar. She looks and acts the part, and is ferociously talented with it. I love her. Her buildings deal in pure, unsettling beauty. First she invented a new architecture; now she is building it, everywhere from Abu Dhabi to Guangzhou. She is so busy, she employs nearly 200 people to help get her stuff designed. I’m happy that Melvyn Bragg is doing a South Bank Show on her this very evening. But I find the hysteria around her and her globe-encircling colleagues a bit relentless.

A couple of weeks earlier, I had attended the coronation of Richard Rogers – Lord Rogers – as winner of thisyear’s Pritzker prize (Hadid already had it). The US-funded Pritzker is the world’s glitziest architecture award, and this year its bandwagon rolled into London. No expense was spared.

They flew in the big hitters of world architecture. There was Nouvel. There was Piano, Foster, Jacques Herzog, Rafael Vinoly. The list, many of them fellow winners of the gong, went on and on. Indeed, there is a tendency among world cities desperate for international status to look no further than the back list of Pritzker laureates when picking the designers of their star buildings. Thus, Abu Dhabi is getting itself not only a Gehry Guggenheim, but a Nouvel Louvre, a Hadid performing-arts centre, a Tadao Ando maritime museum and a recreation of Venice’s Biennale gardens, among much else. It is telescoping the usual centuries of cultural development into a decade.

It’s when architects get to the point where you can’t keep track of all their work any more that the alarm bells start to ring. Big, important international landmarks have always been built, but they used to arrive rarely. There was nothing much between the Sydney Opera House competition of 1956 and the Pompidou Centre competition of 1970, for instance. Stuff got built, sure. Cultural buildings leavened the bread of spec office blocks; America went through a superscraper phase.

Cities went on expanding. But Rogers winning the Pritzker this year was especially poignant because it is now exactly 30 years since the Pompidou Centre was opened. That building – a romantic competition win for Piano and Rogers, when both were, as Rogers happily admits today, more or less unemployed – ushered in the modern era of the city-defining icon building. Nobody knew what to make of the Pompidou Centre at first. Then they saw the visitor numbers. Then everybody started wanting something like that.

What everyone calls the “Bilbao effect”, after the jump-start impact Gehry’s Guggenheim had on the world perception of that grimy industrial city in the late 1990s, was the same as the Pompidou effect or the Sydney Opera House effect. Cultural buildings as giant sculptures, as identifiers, three-dimensional logos. That’s the aim. Those architects who provide such buildings become fêted around the world. And, of course, there is a lot more world to supply than there used to be. Nobody used to build in China or Moscow or Kazakhstan. Dubai was a desert strip with a few fishing boats. Air travel was expensive. People tended to stay in their own countries more.

Offputtingly dull though Global Cities is for anybody not obsessed with numbers and analysis, it does make one important point: such is the growth of the world’s cities that, for the first time, more than half of the world’s population lives in them. That has nothing to do with landmark buildings or the globetrotting signature architects who provide them. It is all to do with finding ways to accommodate everyone. When it comes to the way people live, good ordinary buildings count for a lot more than the headline sculptural stuff. Clean air and water count for a lot, too. But that’s not something you get fees for designing.

I’m thinking about good housing projects by volume housebuilders – such as the Accordia development, in Cambridge, for Countryside Properties by the architects Feilden Clegg Bradley; or good new schools, such as the Marlowe Academy, in Rams-gate, by BDP; or just better offices, such as the Bankside 1/2/3 development, behind Tate Modern, by Allies and Morrison. None of these is a landmark – all try just to make the everyday a bit better.

So, deliciously and unusually, London is host to two remarkably different exhibitions on architecture. At Tate Modern, you find the grimy reality of city life, dressed up a bit. At the Design Museum, you get the full-on adoration of the architectural superstar, Hadid as the icing on the urban cake. Is there any possible way of reconciling these two approaches?

Funnily enough, there is. It’s at Tate Modern, and it is Coates’s Mixtacity. Slyly, he has imagined a megalopolis where every building is a landmark of one kind or other. Impossibly, there is nothing average to be found. Every little bit of it contrives to be special. Now that really is clever. And disturbing. Because when every object you see around you, stretching to the horizon, is special, what on earth happens to the notion of the ordinary?

Global Cities, Tate Modern, SE1, until Aug 27; Zaha Hadid: Architecture + Design, Design Museum, SE1, until Nov 25

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