Boston or New York?

Neither city is a beach destination, but New York gives you more for a hot day. The subway runs straight to the boardwalk and old rides of Coney Island and the long surfing beaches of the Rockaways, and the water is noticeably warmer.

Boston has Revere Beach on the Blue Line and small harbour beaches, but its best sand, such as the dunes of Crane Beach, is out on the North Shore. The colder Atlantic there means a quick dip rather than a long swim.

Boston is at its best with seafood: Duxbury oysters, fried clams, lobster rolls and chowder, plus cannoli and red-sauce dining rooms in the North End. Beyond the sea, though, it has little that is its own, and it is expensive at every level.

New York operates on another scale. Whole neighbourhoods cook the food of the communities that live there, from Flushing to Arthur Avenue, and fine dining sits above them. Its everyday classics, from bagels to halal carts, also make eating well cheap in a way Boston cannot match.

Boston is the place to see the colonial and Revolutionary past. The Freedom Trail links the Old State House, the Old North Church and the USS Constitution, and Beacon Hill and Back Bay keep their nineteenth-century streets almost intact. The Museum of Fine Arts and the Gardner are a strong pair.

New York goes deeper. The Met, MoMA, the Natural History Museum and the Cloisters could each fill a day, and the Statue of Liberty, the Brooklyn Bridge and Grand Central are landmarks known worldwide. Little of its colonial town survives, so the history you walk through is mostly the cast-iron fronts of SoHo and the tenements of the Lower East Side, but there is far more of it to see.

A night out in Boston means a pub. You might choose an Irish bar near Faneuil Hall, a sports crowd around Fenway or a student bar in Cambridge, but last orders come by 2am and the T has stopped soon after midnight.

New York keeps going all night. Trains run around the clock, cocktail bars and dives fill the East Village, rooftop bars look over Midtown, and in Williamsburg and Bushwick the dance-music crowds stay out past dawn. For anyone who wants late nights, the gap between the two cities is enormous.

The two are close here, but the outdoors feels different. Boston's is coastal: Olmsted's Emerald Necklace, sailing on the Charles, ferries to the Harbor Islands, and whale-watching trips to see humpbacks at Stellwagen Bank.

New York's green space is built around its great parks, Central and Prospect, and its reclaimed waterfronts such as the High Line. Its edge is proper hiking. A train up the Hudson brings you to the steep climbs of Breakneck Ridge, which is wilder than anything near Boston.

Both cities have a long list of trips out, and the difference is in the kind. From Boston you visit small old towns: Salem's witch-trial history, the battlefields and writers' houses of Lexington and Concord, the fishing harbours of Rockport and Gloucester, and further out the mansions of Newport.

From New York you can reach a whole second city, Philadelphia, along with Princeton and Yale's New Haven, while the Hudson Valley adds Gilded Age estates and art at Dia Beacon and Storm King.

Both cities work well with children. The New England Aquarium, the Museum of Science and the swan boats in the Public Garden give Boston plenty of choice, and its safe, flat centre makes the days easy.

New York has the bigger headline sights, with the dinosaur halls, the Bronx Zoo and the free Staten Island Ferry. The catch is getting around: stair-only stations, small hotel rooms and the noise of Midtown make it harder going with little ones.

In both cities you can leave the car behind, but New York is the easier one to move around. The Manhattan grid is hard to get lost in, the subway reaches four boroughs and runs all night, and Citi Bike and the ferries fill the gaps.

Boston's old centre is a pleasure to walk, with the Freedom Trail laid out as a walking route. Beyond it, the ageing T is slow in places, the Green Line crawls, and service stops around midnight.

Boston's shopping centres on Newbury Street's brownstone boutiques, with the Prudential Center malls and the antiques of Charles Street nearby. It is solid, and clothing is free of sales tax up to a set amount, but few people would plan a trip around it.

New York is one of the world's great shopping cities. It has the Fifth Avenue flagships, the luxury houses on Madison, Bergdorf Goodman and Macy's, the designer streets of SoHo, and Greenpoint for records, vintage and young designers.

Both cities are expensive, and Boston works out a little kinder on the budget overall. Its centre is compact enough that taxis are rarely needed, and the Freedom Trail and the parks are free. Even so, rooms and meals stay costly, and there is no real cheap option.

New York's Manhattan hotels are the bigger drain. It does have more ways to eat cheaply, with slices, carts and the restaurants of Queens, and staying in Brooklyn or New Jersey cuts the cost of a room without making the trip harder.

Boston is a serious city for classical music. The Boston Symphony Orchestra plays in Symphony Hall, whose acoustics are among the best anywhere, the Handel and Haydn Society specialises in early music, and Berklee students fill the small jazz rooms.

New York simply offers more of everything. Broadway, the Met Opera, the Philharmonic and New York City Ballet at Lincoln Center, and Carnegie Hall would be enough on their own. Village jazz clubs, Harlem gospel and the Brooklyn Academy of Music add more, so there is a strong choice every night.

Neither city is restful, but New York has a bathing culture Boston lacks. There is the old Russian and Turkish bathhouse in the East Village, banyas in Brighton Beach and Korean jjimjilbang spas a short trip away.

In Boston, relaxing means a Back Bay day spa or a slow walk through the Public Garden or the Arnold Arboretum. Visitors who want a truly quiet break usually leave for an inn on Cape Ann.