It's Madrid vs Barcelona – and we're not just talking football

They are bitter rivals on the pitch – and in the battle for Spain's tourist millions. Now the proud capital is fighting back against the confident Catalan upstart

Barça are coming to town. My visit to Madrid coincides with the second leg of the most passionate clash in European club football. Having lost away to Barcelona earlier in the season, Real Madrid are forced into the role of underdog for the fixture at home. And they don't like it. The reflex cockiness of the city's residents is edged with anxiety. There is dread in the barrios. Fear stalks the boulevards. But the game is only one measure of an inter-city rivalry that runs deep. Yes – deeper even than footie.

Cosmopolitan, confident and facing the future with a huge grin, Barcelona presented an irresistible proposition when it hosted the highly successful 1992 Olympic Games. Ever since, judged as a tourist destination, the Catalan capital has given the country's capital a good kicking.

The notion of Madrid being relegated to second-city status is intolerable to proud Madrileños. It cannot be left unanswered. The city's resurgent ambition hits you immediately on arrival at Barajas airport – Richard Rogers' Terminal 4 is a powerful statement of intent. It is an undisputed winner, walking away with the Stirling Prize in 2006 and garnering plaudits from critics and passengers alike.

This building alone is worth the price of the ticket to Madrid. The outstretched bird's wing roof glides over incoming passengers and seems to float in a receding wave as far as the eye can see. It is monumental in the way that buildings of this size have to be, but the mega-tonnage of concrete and the steel is warmed up by the bamboo finish of the undulating ceiling and the orange and lemon highlights of the supporting stanchions. Arriving has never been this much fun.

"Madrileños are open people but they are proud," says my friend Miriam Cara, who lives in the city. "Proud of their heritage, their food and wine. That comes first, but their second characteristic is showing off. They love to show off."

How they must also love the new (2005) extension of La Reina Sofia Museum. It is a screaming extrovert of a building. Architect Jean Nouvel's blood-red atrium overwhelms the original 18th-century hospital that housed the museum. As art gallery extensions go this is no small carbuncle planted on the face of an "elegant friend" – more like straight GBH with a pair of nunchucks. It is a bold and brilliant clash of colours, styles and materials. If forced to stand in the middle of the new extension's forecourt, Prince Charles would no doubt have a seizure. Not so the Spanish royals; Queen Sofia seems amused enough by her museum to have shown it off to Carla Bruni-Sarkozy during a state visit last month.

While the Picasso Museum in Barcelona can boast more than 3,500 of his works, La Reina Sofia has the one that trumps all – Guernica. The painting has a dedicated wing to itself. I arrive at the museum early enough to be able to walk straight in, but an hour later a queue the length of two corridors has formed and face-time with the canvas is being rationed.

Visitors must pick their way through a video presentation, then an ante room, then a gallery with Picasso's studies and only then can they enter the inner sanctum. It is a big room – the painting's dimensions (11 feet by over 25) demand the space. A hushed awe prevails. After the build-up, the painting itself is almost an anti-climax.

Initially, at any rate, I cannot shake off a sense of overfamiliarity – the panicking horse, the shark tooth flames, the broken bodies, the dead baby, the screaming mother are already etched into my brain; they are a part of me. I seem to be looking at a reproduction. Then slowly the size and power of the nightmare vision take effect. There is no escape, nowhere to run. No longer simply about the bombing of Guernica in the Spanish civil war, these slashed lines are a concatenation of all the indelible images of horror from the darkest century in human history. Later on the top floor I stand in front of a series of three brightly coloured canvases, also by Picasso, called The Painter and The Model. After Guernica they seem merely decorative.

In the Rastro Market in the Latina district I find posters (probably fakes) celebrating the Condor Legion of the Luftwaffe that wrought the carnage of Guernica. They are a short sharp reminder that this was the Caudillo's power base, that Real Madrid was his team and that much of the vaunted Spanishness of the city is still tainted by association with Franco's fascism.

Like flea markets the world over, the Rastro is an anarchic mess of hippie flotsam, any old iron and antiquities of dubious provenance. But examined closely, the cascade of objects is revelatory. Madonna and child figurines vie for attention with biscuit tins, clown dolls, majolica tiles and rusty nails. There are stalls offering flamenco knickknacks and others that enshrine bullfighting. Blood and sand. Passion partnered with cruelty. Few markets tell such vivid stories about their host city.

The after party is held in the many bars and cafés of La Latina that fringe the Rastro. Tables, chairs, shoppers and loud conversation spill on to the interstices of the back streets. Ice-cold canas (beer served in thimble-sized glasses) and a vast array of tapas are consumed. Madrileños are rightly proud of their street food, but they will also point out the city is no slouch when it comes to stylish high-end restaurants.

The tasting menu at Michelin-starred Basque chef Eneko Atxa's new residency in the Hotel Villa Magna is both dinner and cabaret rolled into one. Early in the 12-course performance we are presented with what the menu describes as "Oyster with iodized gel, pickleweed and natural sea aromas". Vicente the waiter produces the dish with the flourish of a conjurer, pouring sea water on to concealed chips of dry ice. It "smokes" away for 15-odd seconds filling the nostrils with those crucial "sea aromas", but the real intention I suspect is to elicit oohs and aahs from spellbound diners.

The volcanic "Vegetable Garden" – tomato pulp magma, dried cinder petals of some flower or other and desiccated beetroot to form the gunpowder "sand" – charms my dinner companion who describes it as "food from the fairies" but it strikes me as a salad without a cause. I am more taken with the "Egg cooked inside out with truffle juice". This is an egg yolk with its very own dark truffle baby inside (conceived with a hypodermic needle). The yolk explodes in the mouth, rich, truffly and horribly moreish. Vicente the apprentice chuckles politely as we finally succumb to his master's wiles.

The magic of Madrid is a slow burn compared with the razzmatazz of Barcelona. But the capital holds a few aces up its sleeve. And the Retiro Park on a sunny spring day is one of them. The 300-acre space is a resource for the whole city, all social classes, all generations, all nationalities – where all are equal in the pursuit of hedonism.

There are drummers, dancers, bladers and bathers; cyclists and rowers, jugglers and snoggers. Snapshots include the little princesses in plaid skirts, jackets and cardies being marched into the sundrenched park by their equally immaculately turned-out mummy. Next up – a gay couple in tight shorts and little else are having such a dramatic tiff (the slap is audible from 30 feet) that I suspect they are rehearsing a play. In the Palacio de Cristal gallery, a more conceptual performance has a life-size panda bear/man dangling from a wire, while between the trees American expats play béisbol (baseball) and on the lake, in front of the pompous monument to King Alfonso XII, stressed dads row their families around in little circles. The park is heaving but it presents a vision of a city at ease with itself.

Some Madrileños even kick a football – despite the humiliating result of the previous evening's game in the Santiago Bernabéu stadium. Barça ran riot and thrashed the home team 6-2. It is an unequivocal disaster for Real Madrid. My verdict on Madrid vs Barcelona is less emphatic. It is, as the pundits might put it, a score draw. The underdog done well.

COMPACT FACTS

How to get there

British Airways (0844 493 0787; ba.com) has daily flights to Madrid from £103 return.

Villa Magna (0034 91 587 1234; hotelvillamagna.com) offers a double deluxe room from €374 (£326) per night.

Further information

Spanish National Tourist Office (020-7486 8077; tourspain.co.uk).