Chicago or Washington DC?

Chicago has a proper summer beach scene, which Washington does not. More than twenty sandy strands line Lake Michigan inside the city limits, from Oak Street Beach under the Gold Coast towers to the volleyball courts at North Avenue, and in July and August a swim fits easily between museums.

Washington's rivers are not for swimming. The nearest sand is on the Chesapeake around Annapolis, and the Atlantic resorts are a weekend away, so most visitors there make do with the hotel pool.

Chicago has the stronger food city and a cuisine of its own: deep-dish and tavern-cut pizza, Italian beef, the ketchup-free hot dog. Pilsen, Devon Avenue and Argyle Street add serious Mexican, South Asian and Vietnamese cooking, and the fine dining is among the best in the country.

Washington eats well, but more broadly than distinctively. Its standouts are the Ethiopian restaurants of Shaw and U Street, the half-smoke, and Chesapeake crabs and oysters in season, with Eastern Market and Union Market good for grazing. Downtown, more of the dining is business lunches.

Washington has the edge, mainly because of its free museums. The Smithsonian buildings along the Mall, the National Gallery and the monuments from the Capitol to the Lincoln Memorial add up to more sightseeing than Chicago can offer, and the free entry means you can drop into a museum for just an hour.

Chicago's strength is different. It is one of the world's great architecture cities, from the Rookery to Mies van der Rohe, best seen on a river cruise, and the Art Institute's Impressionists rival anything in Washington. It is excellent on buildings and art, but has less history and fewer landmarks.

Chicago is clearly the better night out. Late licences keep bars pouring until 4am, the neighbourhoods each have their own scene, from Wicker Park dives to River North clubs and Northalsted, and the house music heritage gives the dance floors real character.

Washington's going out is livelier than its reputation, centred on 14th Street, U Street and rowdy Adams Morgan. But it closes earlier, peaks from Thursday to Saturday and leans towards after-work happy hours.

Washington is the greener base. Rock Creek Park runs a wooded valley right through the city, the canal towpath follows the Potomac for hundreds of kilometres, and the Great Falls gorge and the Shenandoah ridges are close enough for a day. Spring blossom and autumn colour add to it.

Chicago's outdoors is essentially the lake: a 29km shoreline path for walking and cycling, park lagoons and good birding. Beyond that the land is flat, with the Indiana Dunes the nearest proper escape.

Washington wins easily on day trips. Old Town Alexandria is a Metro ride away, Mount Vernon, Baltimore and Annapolis are close, and Gettysburg, Antietam and Harpers Ferry put the Civil War within reach. Philadelphia's Independence Hall is a fast train away.

From Chicago the options are thinner and need more effort. Milwaukee by train and the Wright houses of Oak Park are the easy ones, with Lake Geneva and the Michigan harbour towns for anyone with a car.

Both are good with children, in different ways. Chicago packs its attractions into big, full-day outings: the coal mine and U-boat at the Museum of Science and Industry, the Shedd's belugas, Navy Pier's Ferris wheel and, in summer, lifeguarded beaches.

Washington wins on cost and ease. Nearly everything is free, from the Natural History dinosaurs to the National Zoo, so short visits are no loss, and the Mall gives children space to run. Its summer heat is the main drawback, as Chicago's winter cold is there.

Neither city needs a car, and both have flat, gridded centres. The difference is in the details. Chicago's L runs straight from both airports and loops around downtown, but its lines point into the centre, so travel between neighbourhoods often means a long bus ride.

Washington's Metro is cleaner and has lifts at every station, though Georgetown has no stop, and the distances along the Mall are longer than they look. Bike-share helps in both cities, along the lakefront in one and between the monuments in the other.

Chicago is the better shopping city. The Magnificent Mile has flagships and vertical malls, Oak Street has the luxury labels, and the old Marshall Field's store on State Street, under its Tiffany ceiling, is worth seeing for itself. Wicker Park and Andersonville add independent boutiques and vintage.

Washington's shopping is a pleasant extra. It has Georgetown's brick-fronted M Street, a luxury block at CityCenterDC, and weekend craft stalls at Eastern Market, with the Smithsonian shops good for gifts.

Both are expensive, with costly hotels, taxes and tipping, and neither is a cheap trip. They save you money in different ways. Washington's big saving is sightseeing, since the museums, zoo and memorials cost nothing.

In Chicago the savings are in eating: taquerias, hot dog stands and pizza places keep meals cheap, and the beaches and Lincoln Park Zoo are free. Leaving the Loop or avoiding summer cuts room costs, just as staying in Arlington does in Washington.

Chicago's stage is a reason to go in itself. The Chicago Symphony is world class, the Lyric Opera stages a full season, Steppenwolf and the Goodman lead a deep theatre scene, and Second City improv runs every night. Electric blues and late jazz sets give its music a sound of its own.

Washington has more to see than most visitors expect. Arena Stage, the Shakespeare Theatre and Ford's Theatre lead its theatre, U Street has the music, and go-go is its local sound. It also has the open-air lawn at Wolf Trap. But it is a good extra rather than a draw.

Neither city is built for unwinding, but Chicago has the edge with a real bathing tradition: the century-old Russian-and-Turkish bathhouse in Wicker Park and a Korean jjimjilbang in the suburbs, plus warm conservatories for winter.

Washington offers hotel spas and yoga studios, and its calm comes from open spaces such as the Tidal Basin at dawn, the Dumbarton Oaks gardens and the Arboretum.