Washington DC or New York?

New York has real ocean beaches you can reach by subway: Coney Island with its boardwalk and old rides, Russian-speaking Brighton Beach, and the long, open Rockaways where people surf. Jones Beach and Long Beach on Long Island are about an hour further out. It is a summer break from the city rather than a beach vacation, but you can swim in the Atlantic on an ordinary afternoon.

Washington has nothing like this. Its rivers are not for swimming, the small, brackish Chesapeake beaches near Annapolis are an hour's drive away, and the proper Atlantic resorts take about three hours, which makes them a weekend trip.

New York's food scene is wider and deeper. Whole immigrant communities cook their own food across the boroughs, from Arthur Avenue Italian to Caribbean Crown Heights, and the city's own classics, the slice, the bagel and the deli pastrami, cost little and are everywhere. Above that sits one of the world's great fine-dining scenes.

Washington eats well but on a smaller scale. Its standouts are the Ethiopian restaurants of Shaw and U Street, pupusas in Columbia Heights, the half-smoke, and summer crabs and oysters from the old Southwest waterfront fish market. Downtown, much of the dining leans towards steakhouses and business lunches.

Both cities could fill a week with museums, but in different ways. New York's strength is the depth of its great art collections, the Met, MoMA and the Museum Mile houses, along with a cityscape of brownstones, cast-iron SoHo and Lower East Side tenements. Most of the big museums charge for entry.

Washington tells the national story in one place. The Smithsonian museums and the National Gallery line the Mall, nearly all of them free, so you can drop in for an hour. Around them stand the Capitol, the Lincoln Memorial and Arlington Cemetery. The old streets of Georgetown are pleasant but quiet, and the monuments are what you remember.

New York lets you choose the kind of night as well as the neighbourhood. There are speakeasy-style cocktail bars on the Lower East Side, quiet wine bars on the side streets of the West Village, and rooftops in Midtown and Long Island City that look straight out over the skyline. The gay bars of the Village have a history that goes back to Stonewall, and the Meatpacking District has bottle-service rooms for a dressed-up night.

Washington's nightlife is better than its reputation, but there is less of it and it ends earlier. The 14th Street and U Street corridor has cocktail bars, rooftops and late dance spots. Adams Morgan is the rowdier strip, H Street has the dive bars, the Wharf has riverside beer gardens and Dupont Circle has long been the centre of LGBTQ+ life. It is busiest from Thursday to Saturday, the bars close in the early hours, and early in the week most of the drinking is after-work happy hours.

Washington is the greener city. Rock Creek Park runs a wooded valley through its middle, the C&O Canal towpath follows the Potomac for hundreds of kilometres, and half an hour upriver Great Falls has cliff paths, climbing and whitewater. Shenandoah and the Blue Ridge are close enough for a day of ridge walking.

New York's outdoors is mostly designed: Central and Prospect parks, the High Line and the converted waterfronts, plus birdwatching at Jamaica Bay. For a real climb you take the train about ninety minutes up the Hudson to Breakneck Ridge.

Both have plenty within a day's reach, and they share Philadelphia, which is closer and easier from New York. Otherwise New York's day trips lean towards art and old wealth: Gilded Age estates along the Hudson, Dia Beacon and Storm King, and Yale's museums in New Haven.

Washington's are about history. Old Town Alexandria is a Metro ride away, Mount Vernon and Baltimore's Fort McHenry are close, and the Civil War battlefields at Gettysburg, Antietam and Harpers Ferry are each an hour or two out, though for those you will want a car.

New York gives children more to do, and Washington makes the days easier. In New York there are the dinosaur halls and planetarium, the vast Bronx Zoo, the aircraft carrier on the Hudson and the free Staten Island Ferry. The price is paid in getting about: subway stairs with a pushchair, small hotel rooms and the noise of Midtown.

In Washington the museums and the National Zoo are free, so you can leave when the children have had enough. Every Metro station has a lift, and the Mall is open lawn for running about. What tires families out is the long, exposed walk between the monuments in summer.

New York is the easier city to get around without a car. Manhattan's grid is easy to walk, and the subway runs around the clock across four boroughs, with ferries and bike docks filling the gaps. The trade-offs are a map that takes some learning, stations with only stairs that turn stifling in summer, and awkward airport journeys.

Washington's Metro is cleaner and simpler, has lifts everywhere and runs straight to Reagan National Airport. It thins out late at night and at weekends, though, and skips Georgetown entirely, and distances across the flat centre are longer than they look.

For shopping there is no contest. New York covers every level, from the Fifth Avenue flagships and the luxury houses on Madison Avenue to Bergdorf Goodman and Macy's, SoHo's design brands, Nolita boutiques and the vintage and record stores of Williamsburg.

Washington's shopping is a pleasant sideline. Georgetown's M Street and the luxury block at CityCenterDC are the main streets, Eastern Market has weekend flea stalls, and the Smithsonian shops are good for books and prints. There is no great department store to seek out.

Neither is a cheap city, but New York is the harder one on the wallet. Its Manhattan rooms are small and dear, and tax and tips are added to every bill, so savings come from slices, carts and Queens restaurants, the free ferry and parks, and staying in Brooklyn or New Jersey.

Washington's hotels and restaurants are also priced for expense accounts. The difference is that its main sights are free: a day at the Smithsonian, the National Gallery and the memorials costs almost nothing beyond a Metro fare.

New York is in a league of its own here. Broadway and Off-Broadway, the Met Opera, the Philharmonic and City Ballet at Lincoln Center, Carnegie Hall, a century of Village and Harlem jazz, Sunday gospel and free Shakespeare in the park mean there is something worth seeing every night.

Washington's strength is theatre: Arena Stage, the Shakespeare Theatre Company, the Folger's small playhouse and Ford's Theatre, where Lincoln was shot. The National Symphony gives it a proper classical season, and U Street keeps Duke Ellington's musical legacy and go-go alive. It is a good night out rather than a reason to book.

New York has a bathing tradition that Washington simply doesn't have. The East Village bathhouse has offered steam, a hot stone sauna and an ice plunge since the late 1800s, Brighton Beach has its Russian banyas, and the big Korean jjimjilbang in Queens and New Jersey are worth the trip for heated rooms and pools.

In Washington, wellness means hotel spas, day spas and yoga studios in a town that runs on office hours. Rest comes from its quiet open spaces instead: an early walk around the Tidal Basin, or a bench in the Dumbarton Oaks gardens or the National Arboretum.