Amsterdam or London?

Neither city is somewhere to plan a beach vacation, but the seaside differs in kind. From Amsterdam the long sandy shore at Zandvoort and Bloemendaal, backed by dunes, is only half an hour by train. From London, Brighton takes about an hour and is pebble, though Margate and Whitstable offer sand.

Swimming in town follows local habits: Amsterdammers head for the IJburg beaches and lakes such as the Sloterplas on hot days, while Londoners use the outdoor lidos and the Hampstead Heath ponds, which some swim in all year.

London is the far better place to eat. Bangladeshi cooking on Brick Lane, Turkish grills in Green Lanes, Punjabi food in Southall, Caribbean and West African kitchens south of the river, Borough Market and a strong fine-dining and modern British scene give it a range Amsterdam cannot match.

Amsterdam's strengths are narrower: Indonesian rijsttafel, Surinamese roti, herring from street stalls and stroopwafels at the Albert Cuyp. Where it is most enjoyable is drinking, in old brown cafés and jenever tasting rooms over a borrel of beer and bitterballen.

Both are outstanding, but London goes much deeper. Amsterdam concentrates its riches: the Rijksmuseum, the Van Gogh Museum and the Stedelijk around one square, the Anne Frank House and a UNESCO-listed canal ring that is itself the main sight, all manageable in a few days.

London has the British Museum, the National Gallery, the V&A and both Tates, most free to enter, plus a thousand years of landmarks from the Tower and Westminster Abbey to St Paul's and Greenwich. It is less uniform to look at than Amsterdam, but a week there barely scratches the surface.

London offers more, spread across distinct districts: Soho for late bars and the gay scene, Shoreditch, Hackney and Dalston for clubs and warehouse parties, Brixton and Peckham for big venues, and thousands of pubs everywhere. Its weekends in particular are hard to beat.

Amsterdam is smaller but punches above its size in electronic music, with all-night clubs in old industrial buildings and in Noord, and the Amsterdam Dance Event every October. Its more relaxed evenings are spent on canal-side terraces in the Jordaan and De Pijp.

London has more green space within reach. Richmond Park with its deer, Hampstead Heath's views over the skyline and Kew's gardens are proper escapes, and the Chilterns, North Downs and South Downs are an hour or so away with marked footpaths.

Amsterdam's outdoors is flatter and quieter: a ferry and a bike ride into Waterland's meadows and wooden villages, the Amstelveen woods of the Amsterdamse Bos, and the dunes of Zuid-Kennemerland with their bison. It is lovely by bike, but it offers less variety.

Both are superb bases for day trips, and the difference is in distance and character. From Amsterdam everything is close: Haarlem is a quarter of an hour away, and Leiden, Delft, Utrecht, The Hague, windmills at Zaanse Schans and Kinderdijk, and the Keukenhof in spring are all easy, with Antwerp in reach too.

From London the trips run longer but are grander: Oxford and Cambridge in about an hour, Windsor Castle, Bath's Roman baths, Stonehenge with Salisbury, and Canterbury and the castles of Kent.

London has more for children, and much of it is free: the dinosaurs at the Natural History Museum, the Science Museum, the Young V&A, the pirate-ship playground in Kensington Gardens and the zoo in Regent's Park. Legoland and the Harry Potter studio tour lie just outside. The drawbacks are the long distances and Tube stairs with a buggy.

Amsterdam is smaller and calmer, with Artis, the NEMO science museum, city farms and pancake houses, but fast bikes and unfenced canal edges mean keeping a firm hand on small children.

Both are easy without a car, but in different ways. Amsterdam is compact and flat, so you can walk or cycle between most sights in half an hour, with trams and free IJ ferries to fill the gaps. You just need to watch for bikes.

London depends on the Underground, the Elizabeth line and its buses, with riverboats on the Thames. The network is excellent, but the city's size means longer journeys, crowded rush hours and many stairs.

London is one of the world's great shopping cities and Amsterdam is not in the same league. Savile Row tailoring, the Bond Street luxury houses, department stores such as Liberty, Harrods and Fortnum & Mason, and markets from Portobello Road to Columbia Road could fill several days.

Amsterdam is best for browsing small independents in the Nine Streets and the Jordaan, plus the Waterlooplein and Noordermarkt markets, with Delft blue and Dutch cheese as the classic things to bring home.

Neither is cheap, but Amsterdam is somewhat easier on a budget. Its central rooms and tourist tax are steep, but walking and cycling cost little, and staying in Haarlem or Utrecht is a realistic way to save.

London is heavier still, with small, expensive hotel rooms, high fares per journey and costly theatre seats. Its saving grace is that the great museums and parks are free, which helps a careful traveller but rarely makes the total cheaper.

London is in a class of its own here. It combines the West End, the National Theatre, the Globe and fringe stages above pubs with the Royal Opera House, five major orchestras, the Proms at the Royal Albert Hall and Wigmore Hall for chamber music.

Amsterdam's strength is classical music, led by the Concertgebouw and its orchestra, with the opera house on the Amstel, the Bimhuis for jazz, and Paradiso and the Melkweg for touring bands. Its theatre is mostly in Dutch, however, which limits it for visitors.

Neither city is somewhere people go to unwind, and their bathing traditions differ in kind. Amsterdam's are the large day spas and saunas on the city's edges, mostly mixed and nude in the Northern European way, and its calmer moments come early in the morning on the quieter canals or on a ferry across the IJ.

London's are older and more formal: historic early 20th-century Turkish baths in Bayswater and Islington, with steam rooms and plunge pools under tiled vaults, and full spas in the grand hotels of Mayfair and Knightsbridge. For a proper soak in thermal water, Bath is about an hour and a half away by train, and in town a quiet weekday gallery or a cold lido does the rest.