The new gulf war: which state can spend its oil trillions faster?

They sit on a generous slice of the world's natural resources, are just a two-hour drive from each other and have trillions of dollars burning a hole in their pockets. Now, they want a piece of your business, your holiday, the films you watch and even the football team you support. And the only people wealthy enough to stop them are each other.

This week, a sheikh from Abu Dhabi bought up the Premier League football team Manchester City (and Dubai is preparing to pounce on Liverpool FC at any moment), while both have ambitions to become centres for the Western realms of modern art and film.

Welcome to the battle of the petro-bucks being waged by the oil emirates of the Middle East – the established billionaires' playground of Dubai and the newer rich kid on the block, Abu Dhabi. From skyscrapers half a mile high to building islands in the formation of the world map, the two cities have become known for engaging in some of the most costly prestige projects on the planet.

A curious quirk of the world's rising oil prices, which topped $150 a barrel briefly this summer, is that this has not been mirrored in an increase in the cost of producing crude. Despite the freedom with which they have invested in everything from books to ports, it has made it almost impossible to spend a hole in their mounting fortunes.

Their growing piles of cash have meant the two emirates have had to find ever more imaginative ways of investing it. While projects in the past have been devices to establish themselves as top business and leisure locations, they have increasingly turned to extreme displays of wealth for its own sake.

Next up are some of the world's greatest sporting events. Dubai already hosts a key golf tournament, but both have their sights aimed higher. Abu Dhabi is to be home to Formula One next year and there is even talk of a Dubai Olympic bid. It may not be long until Brad Pitt et al will have to ditch the chic Hollywood hills and decamp to make the blockbusters in an Abu Dhabi studio. It is all part of an explicit aim to become a hub of Western cultural industry.

At times, the sheer cost of their projects has meant their conspicuous use of wealth has moved from the shamelessly luxurious to the openly gratuitous. Dubai's multibillion-dollar project to construct a series of man-made islands in the shape of the world map is perhaps the most extreme example to date.

If the spending has become a mania for them, that is because of the impermanence of the source on which the wealth is based – oil. The drive to press their money into every hand that will receive it is designed to give the emirates something to show for their good fortune, once their rivers of black gold run dry.

Emirates' investments

Sport

Abu Dhabi

Sheikh Mansour Bin Zayed al-Nahyan, the brother of the emirate's ruler, snapped up the Premier League club Manchester City and his front man, Sulaiman al-Fahim, shelled out a British record of £32.5m for the Brazilian striker Robinho. It is to stage Formula One motor racing next year.

Dubai

A takeover of Liverpool FC has been on the cards for some time. The gargantuan Dubai Sports City complex – $4bn (£2.26m) and 50,000,000 sq ft – was thought to have been part of Dubai's efforts to host the 2016 summer Olympics, though no bid was submitted. Its 18-hole championship golf course is to be designed by Ernie Els.

Architecture

Dubai

The city's most ambitious projects are being built not only upwards but also outwards, into the sea. Its artificial islands, the "Palm Islands" and "The World", are created on miles of land reclaimed from the Gulf at a cost of about £15bn. Burj Dubai (Dubai Tower) became the tallest building in the world in 2007, at 2,257ft (688m), and is yet to reach its full height.

Abu Dhabi

The emirate is to create the world's first zero-carbon city. The British architect Norman Foster is behind the building of Masdar. Work began this year and it is expected to take eight years and to cost more than £11bn. Abu Dhabi also bought a 75 per cent stake in New York's Chrysler Building in July.

Media

Abu Dhabi

The Abu Dhabi Media Group created "imagenation abu dhabi" to make eight films a year. The new newspaper The National was launched this year.

Dubai

Its Media City, a tax-free zone, has attracted broadcasters such as Reuters, the BBC and CNN.

Tourism

Dubai

Efforts to attract tourists seeking out luxury have meant that architects have been able to build their dream projects. One hotel, Atlantis, is to open this month. It is a 1,539-room mega-hotel with 17 eating establishments, a water park with an 11 million-litre lagoon and what are claimed to be the ruins of Atlantis. Visitors can even go to Dubai for a holiday to Lyon – Saeed al-Ghandi, a local businessman, enjoyed his visit to the French city so much that he has plans to build a full-scale, £1.37bn working replica back home.

Abu Dhabi

The emirate only paved its first road in 1961 but is partnering its rapid expansion with what the government calls "one of the most impressive constellations of cultural attractions ever assembled". Key to this plan are developments on islands surrounding the city, such as Saadiyat Island (Happiness Island). The island's cultural district will feature some of the world's biggest names in art and architecture. Abu Dhabi is also completing a $254m expansion of its international airport with $6.8bn earmarked for various projects and development.

Transport

Dubai

Dubai's Emirates airline has been around since the 1980s. It has a $30bn fleet and has spent a fortune on sponsorship – £100m for Arsenal FC being one high-profile deal. Dubai also made a £3.3bn deal to buy the ports and ferries group P&O.

Abu Dhabi

Despite each citizen being worth $17m per head, in airline terms it is the poor relation. Etihad Airways is still some way behind Emirates, but it is making a big attempt to expand. This summer, it announced the purchase of up to 95 Boeing wide-body jets and up to 110 Airbus planes.

Culture

Abu Dhabi

The emirate announced last year that it was to have its very own version of the Louvre. Completion of the Abu Dhabi branch of France's premier museum and gallery is expected in 2012, under a $1.3bn agreement between Sheikh Sultan bin Tahnoon al-Nahyan and France's Culture Minister. It will be placed alongside Abu Dhabi's very own version of the Guggenheim, New York's famed gallery, on Saadiyat Island at a cost of $27bn.

Dubai

The Gulf Art Fair, curated by Her Royal Highness Princess Haya Bint al-Hussein, has been its biggest success to date in cracking the art world. Sotherby's and Christie's were tempted over by the state's zero import or export taxes for art. More galleries and an opera house are on the way. It has also been the location for record sales of Arab and regional art – a sculpture by the Iranian artist Parviz Tanavoli fetched $2.8m earlier this year as Dubai's buyers have started to see art as an investment opportunity.