London or New York?

Neither is a beach destination, but New York does much better here. Its ocean beaches are inside the city: Coney Island has its boardwalk and rides, and the Rockaways are longer and draw surfers. Both are on the subway, and the Atlantic is pleasant for swimming from late June to early September.

London's nearest sea is an hour away by train at Brighton, where the beach is pebble and the Channel stays cool. Londoners swim in fresh water instead, in the lidos at Brockwell Park and Parliament Hill and in the Hampstead Heath ponds.

Both cities eat the world through their immigrant communities, but New York goes wider and is better for cheap food on the street. Pizza by the slice, bagels, deli pastrami and halal carts are local classics in their own right, and in Jackson Heights or Flushing one evening of eating can cover several continents.

London is strongest on South Asian cooking, from Brick Lane to Southall, and on Borough Market and the weekend markets in old yards and arches. It also has the pub and the Sunday roast as rituals. The food is excellent, but cheap everyday eating is less of a draw than in New York.

These are two of the world's great museum cities, and the difference lies in era and cost. London's history reaches back a thousand years, from the Tower and Westminster Abbey to Wren's churches, and national collections such as the British Museum and the National Gallery are free to enter.

New York's past is mostly nineteenth and twentieth century, seen in Brooklyn brownstones and the cast-iron streets of SoHo, and its collections lean modern, with MoMA, the Guggenheim and the Whitney. The Met can stand beside anything in London, but most major museums charge for entry.

New York keeps going after London stops. The subway runs all night, and bars stay open into the small hours in the East Village, the West Village and Long Island City, while the warehouses of Williamsburg and Bushwick go on past dawn.

London's weekend nights are first class, in the late streets of Soho and the clubs of Shoreditch and Dalston, and its thousands of pubs are a tradition of their own. But many pubs empty around eleven, and the quieter districts keep sensible hours.

Both are green for big cities, and both need a train for anything wild. London's parks feel closer to countryside, with deer and ancient oaks in Richmond Park and open views from the top of Hampstead Heath. Beyond the city lie gentle chalk downs and beechwoods.

New York's parks are designed landscapes or old waterfronts turned into walks, like the High Line. Its escape is steeper, though: Breakneck Ridge in the Hudson Highlands, about ninety minutes by train, is a real rocky climb, and October brings the autumn colour.

London has the clear advantage here. Oxford, Cambridge and Windsor are an hour or less by train, and Bath, Canterbury, Brighton, and Stonehenge with Salisbury can fill a week with outings that never repeat a theme.

New York has fewer easy targets. The best is Philadelphia and its colonial old town, and Princeton, the Gilded Age estates of the Hudson Valley, Dia Beacon and Storm King are also within reach. The Hamptons make a long day, and Boston and Washington really need an overnight stay.

London makes children's days simpler, mostly because so much is free. The dinosaurs at the Natural History Museum, the Science Museum, the Young V&A and the parks cost nothing, and Legoland and the Harry Potter studio tour are close by. Buses with step-free boarding help with a buggy.

New York has its own big draws in the American Museum of Natural History, the Bronx Zoo and the free Staten Island Ferry. But small hotel rooms, stations with only stairs and the noise of Midtown tire families out faster. Staying near a big park makes a real difference.

Neither needs a car, and both have stations full of stairs that get stifling in summer. The difference is in layout. Manhattan's grid makes it easy to walk between Midtown, the Village and Lower Manhattan, and the subway runs round the clock, though the express and local lines take some getting used to.

London is more spread out, so trips between neighbourhoods take longer. The Underground, the Elizabeth line and the buses link up neatly, though, and a seat on a bus's top deck or a Thames riverboat doubles as sightseeing.

Both are among the world's great shopping cities, with grand department stores, luxury streets and flagship stores. London stands out for tradition: bespoke tailoring on Savile Row and Jermyn Street, Liberty and Fortnum & Mason, the antiques of Portobello Road and the Sunday flower market on Columbia Road.

New York stands out for range and specialist shops. It runs from Fifth and Madison Avenues to the cast-iron boutiques of SoHo, with vintage clothes and records in Brooklyn, plus sneakers, cameras and rare books.

Neither will feel cheap. Hotel rooms in both are small and costly, and theatre seats and drinks add up fast. London saves you money with its free national museums, while New York's museums and observation decks charge, and sales tax and a tip come on top of every restaurant bill.

New York makes up for it with cheap everyday food (slices, bagels, food carts and the restaurants of Queens) and a flat subway fare to anywhere. In both cities, the surest saving is to stay further out on a good line.

The two are equals on quality and differ in flavour. The West End and Broadway are the two great theatre districts, but London leans towards plays, from the National Theatre and the Globe to the fringe stages above pubs, and it has the BBC Proms every summer.

New York's speciality is jazz, with a century of history in the basement clubs of Greenwich Village and the rooms of Harlem. It also has Lincoln Center, Carnegie Hall and Sunday gospel in Harlem churches.

Neither city is built for rest, and both have old bathing traditions that visitors often miss. London has Victorian and Edwardian Turkish baths in Bayswater and at Ironmonger Row, and real thermal waters at Bath, about an hour and a half away by train.

New York has a Russian and Turkish bathhouse in the East Village that dates from the late 1800s, along with Russian banyas in Brighton Beach. It also has large Korean-style spas in Queens and New Jersey, where you can spend a whole day moving between heated rooms and pools.