New York or Shanghai?

Of the two, only New York makes a beach day realistic. Coney Island, Brighton Beach and the Rockaways are at the end of subway lines, and the Atlantic is warm enough for swimming from late June into early September. Jones Beach and Long Beach are about an hour further out.

Shanghai faces the muddy Yangtze estuary, where nobody swims. The nearest thing to a beach is the walled, filtered bay at Jinshan, in an industrial setting, and anything better means flying to Hainan. In practice, swimming here means a hotel pool.

Both are among the best places to eat anywhere. The difference is that New York offers breadth and Shanghai offers depth. New York puts the world's kitchens on one subway map: Fujianese in Flushing, Tibetan in Jackson Heights, Caribbean in Crown Heights. On top of that come its own slices, bagels and deli pastrami, and a fine-dining scene that gets very expensive.

Shanghai goes deep into one country's cooking. Sweet, soy-braised benbang dishes, soup dumplings, shengjian buns and hairy crab in autumn sit alongside regional kitchens from Sichuan to Xinjiang, and breakfast at a street stall costs very little. The cafés of the former French Concession and the neighbourhood wet markets show a slower side of daily life.

New York has far more to see. The Met, MoMA, the Natural History museum and the Guggenheim alone could fill a long stay, and landmarks from the Statue of Liberty to Grand Central are familiar before you arrive.

Shanghai has fewer sights, but they are distinctive: the Art Deco banks of the Bund facing the Lujiazui towers, the shikumen lane houses of the former French Concession, and the bronzes and ceramics of the Shanghai Museum. In both cities the history on show is mostly nineteenth and twentieth century, and for classical China you have to leave Shanghai.

Both stay out late, but New York has more going on, and in more places. Dive bars in the East Village, wine bars in the West Village, gay bars dating back to Stonewall and the warehouse clubs of Bushwick and Williamsburg mean almost every neighbourhood has a mood of its own, and the trains run all night.

Shanghai's nights centre on cocktails, in unmarked speakeasies in the former French Concession and hotel bars above the Bund looking across to Pudong. Its clubs also run until dawn, but the scene is spread out, and drinks in the smarter places cost as much as in any Western capital.

Neither city is wild, but New York gets you into the hills far more easily. Beyond Central Park, Prospect Park and the High Line, a train ride of about ninety minutes up the Hudson reaches the steep climbs of Breakneck Ridge, and October colour in the Hudson Valley is a real draw.

Shanghai sits on the flat Yangtze delta. Century Park, the riverside paths along the Huangpu and the Dongtan wetlands on Chongming Island are pleasant, but the Sheshan hills are only low mounds, and the bamboo forests of Moganshan need more than a day.

Shanghai is well ahead here. High-speed trains reach the gardens of Suzhou in about half an hour, West Lake in Hangzhou in about an hour and Nanjing's Ming walls in about an hour and a half. Canal towns such as Zhujiajiao and Wuzhen make easy days out among stone bridges and waterways.

New York's options are good, but there are fewer of them and they lie further away. The best are Philadelphia's colonial old town, Princeton, New Haven with Yale, and the Hudson Valley estates, Dia Beacon and Storm King. Boston and Washington really need an overnight stay.

Shanghai is the easier city with children. Disney is on the metro, Legoland and the ocean park make more big days out, the science museum is hands-on, and lifts at most stations make a buggy simple. The drawbacks are the summer heat, the crowds during the national travel weeks around Chinese New Year and early October, and the long distances between sights.

New York has the dinosaur halls of the Natural History museum, the Bronx Zoo and the free Staten Island Ferry. But stair-only subway stations, small hotel rooms and the noise of Midtown make every day harder work.

Neither city needs a car, but they work differently. In Manhattan, the grid lets you walk between much of Midtown, the Village and downtown, and a round-the-clock subway, harbour ferries and Citi Bike cover the rest. On the downside, many stations have only stairs and the airports are awkward to reach.

Shanghai's metro is cleaner and signed in English, with lifts and lines running straight to the airports. The city is so spread out, though, that crossing it often takes the better part of an hour underground. Set up mobile payments before you go, because cash is rarely used.

New York is the stronger shopping trip, with depth at every level. Fifth Avenue and Madison Avenue have the flagships and luxury houses, there are department stores such as Bergdorf Goodman and Macy's, SoHo has the big brands, and Williamsburg and Greenpoint are good for vintage, records and young designers.

Shanghai has its own glossy malls on West Nanjing Road, but its best finds are of a different kind. Chinese designers have boutiques on Wukang Road and Anfu Road, tea and silk are sold around Yu Garden, and fabric markets will tailor a suit or a qipao in a few days.

Shanghai is far easier on the budget. Noodles, dumplings and breakfast snacks are very cheap, the metro and taxis cost little and many museums are free. Only central hotels, cocktails and Western restaurants reach the prices of a global city.

New York is expensive at almost every turn, from small Manhattan rooms to the tax and tip added to every meal. Pizza slices, food carts, the parks, the High Line and the Staten Island Ferry help, and so does staying in Brooklyn, Queens or New Jersey.

For live performance, New York is clearly the stronger choice. Broadway and Off-Broadway, the Met Opera, the Philharmonic and City Ballet at Lincoln Center, Carnegie Hall and a century of jazz in Village basements and Harlem rooms mean a real choice every night.

Shanghai offers what New York does not: acrobatics, Kunqu and Yue opera, and Peking opera at the Yifu Theatre, a house dating from the 1920s. Its Western programme of symphony, ballet and touring musicals is solid, and a few jazz clubs keep alive the memory of the Bund's ballroom era.

Shanghai makes rest easier to find. It has large bath centres where locals spend hours or stay overnight, foot-massage parlours on almost every residential street and clinics offering acupuncture. Tea houses and morning tai chi in the parks add a slower side to a fast city.

New York has its moments: the old Russian and Turkish baths of the East Village, the banyas of Brighton Beach and Korean spas in Queens. But the city's pace works against calm, and quiet usually means a morning in a park or in the gardens of the Cloisters.