Frankfurt or London?

Neither city is for a beach trip, but London at least has a coast within reach. Brighton's pebble shore is about an hour away by train, and Margate and Whitstable have sandier stretches, although the Channel stays cool. In town, the lidos and the Hampstead Heath ponds give London a real swimming culture.

Frankfurt is a full day from the sea. Summer swimming means outdoor pools and gravel-pit lakes such as the Langener Waldsee, which has sandy edges and pleasantly warm water in high summer, but nothing more.

Frankfurt's cooking is hearty and local: Grüne Soße, Handkäs mit Musik and tart Apfelwein at long tables in Sachsenhausen, with the Kleinmarkthalle for sausages and cheese. Bahnhofsviertel adds cheap international food, but the local menu is short and a few meals cover it.

London's strength is its range. Bangladeshi cooking on Brick Lane, Punjabi food in Southall, Turkish grills in Green Lanes and Caribbean kitchens south of the river sit alongside serious fine dining and Borough Market. Over a week you will eat far more varied food in London, though it rarely comes cheap.

Frankfurt gives you a compact, rewarding museum trip. The Städel is the highlight of the Museumsufer, the Senckenberg is excellent, and the rebuilt Römer, the cathedral and Goethe's birthplace stand close together under the tower skyline. Most of the old town was rebuilt after 1944, and two or three days do it justice.

London is on another scale. The British Museum, the V&A and the National Gallery are each worth a day, the landmarks run from the Tower and Westminster Abbey to Wren's St Paul's and Greenwich, and a week only scratches the surface.

Frankfurt's nights out are smaller and come mostly at weekends. The best of it is the techno and house heritage it shares with Offenbach, the cocktail bars of the Bahnhofsviertel, the bars along Berger Straße and summer drinks on the Main banks. Early in the week the city is quiet.

London offers far more choice. Soho stays busy late, Shoreditch and Dalston keep the warehouse-party tradition going, Brixton and Peckham have big venues and rooftop bars, and thousands of pubs fill in everywhere else. Many pubs still close around eleven, but on Friday and Saturday few cities match it.

There is little between them, but the green space sits in different places. London's is inside the city. Richmond Park's deer and ancient oaks, Hampstead Heath's views and the Thames Path are on the Tube, and the Chilterns and the Downs are an hour out by train.

Frankfurt has the Stadtwald on its doorstep and real hills close by. The Taunus beech forests and the Großer Feldberg, at about 880m, are under an hour away, and the vineyard paths of the Rheingau give it the better walking country just outside town.

Both cities sit at the centre of fast rail networks and offer more outings than a week can hold. The difference is in what you see. From Frankfurt, the outings are castles above the Rhine Gorge, Heidelberg's castle ruin, Riesling villages in the Rheingau, and the cathedrals of Cologne, Mainz, Speyer and Worms.

From London, the trips go to the colleges of Oxford and Cambridge, Windsor Castle, Georgian Bath, Stonehenge, and the seaside at Brighton. London's list has more variety, mixing university towns, castles and coast, while Frankfurt's leans towards rivers, wine and great churches.

Frankfurt has a shorter list for children: the Senckenberg's dinosaur hall, the central zoo, the Palmengarten's glasshouses and a boat trip past the skyline, with the Kronberg wildlife park out in the Taunus. Its advantage is a smaller one, ease, since the centre is compact and trams and the S-Bahn take pushchairs without fuss, but a few days use it up.\n\nLondon is the better family choice overall, with enough to fill a week and much of it free.

The Natural History Museum's dinosaurs, the hands-on Science Museum, the pirate ship at the Diana Memorial Playground and Legoland Windsor outside the city cover every age. What it asks is effort: long distances, crowds when schools are out, and Tube stations with stairs that are hard with a buggy.

London's network takes you further. The Underground, the Elizabeth line, buses and Thames riverboats cover the whole city on one contactless card, and the central stretch from Westminster to the South Bank is good walking. The catch is the city's size, with long transfers, stairs and packed rush-hour trains.

Frankfurt is much smaller. Most sights are a few minutes' walk apart, one regional ticket network reaches Wiesbaden and the Taunus, and the airport is only about a quarter of an hour from the centre by train.

Frankfurt is fine for practical shopping. The Zeil has the department stores, Goethestraße the luxury houses, and Berger Straße and Schweizer Straße the independent shops, while stoneware apple-wine jugs make the local souvenir. Nobody goes there for the shopping alone.

People do travel to London to shop. Savile Row tailoring, Liberty and Fortnum & Mason, Portobello Road antiques, Columbia Road's Sunday flowers and the bookshops of Charing Cross Road make shopping a reason for the trip in itself.

Neither city is cheap, but Frankfurt is easier on the wallet. Its high prices are mainly hotels, and they are tied to the trade fairs, so a weekend or summer visit can feel moderate. Cider taverns and market stalls keep meals cheap.

In London everything costs more: small central rooms, pub rounds, theatre seats and fares. Free national museums and parks help a great deal, but even a careful visitor will spend more here.

Frankfurt has a good arts scene. Its opera company is known for bold productions, the Alte Oper hosts the radio symphony orchestra, and old jazz cellars still hold sessions. The season runs from autumn to early summer, so a July visit finds little on.

London is one of the world's two great theatre cities, from West End musicals to the National Theatre, the Globe and fringe stages above pubs. It also has five major orchestras, the Royal Opera House and the Wigmore Hall. Summer brings the Proms to the Royal Albert Hall, so there is no slack season.

Frankfurt itself has no bathing tradition, but it is surrounded by spa towns. Wiesbaden's hot-spring Kaiser-Friedrich-Therme, the thermal baths of Bad Homburg, and Bad Nauheim are all short trips away, and the Palmengarten is a calm spot in town.

London has a few Victorian Turkish baths in Bayswater and Islington, hotel spas, and cold dips at the lidos and ponds. The pace is tiring, though, and the nearest thermal waters are in Bath, about an hour and a half away by train.