When Sheikh Hamed paid £100m for the best residence at London’s One Hyde Park apartment building in 2007, it confirmed the city as the world’s premier deluxe property investment honeypot. But even as Mayor Boris Johnson and Chancellor George Osborne plot to outpace the growth of New York and make London “the greatest city on earth”, as they proclaimed last week, the Big Apple is taking deluxe living to astonishing new heights – and winning the competition to attract the best names in architecture.