Amsterdam or Luxembourg?

Neither is a beach destination, but Amsterdam at least has the sea. The sandy, dune-backed shore at Zandvoort and Bloemendaal is half an hour away by train, with beach pavilions in summer, though the cold and windy North Sea makes it better for walking than swimming. On hot days, locals swim at IJburg's city beaches and in the Sloterplas.

Luxembourg has no coast at all. Swimming means lakes, either the Upper Sûre reservoir or the old gravel pits at Remerschen. Both are warmer than the North Sea in high summer, but they make a short outing, not a beach day.

Amsterdam's best food comes from its trading past, so the dishes to look for are Indonesian rijsttafel and Surinamese roti, along with herring and stroopwafels from the markets. Its drinking culture has real character, from the old brown cafés to the early-evening borrel of beer and bitterballen, and De Pijp and the Jordaan are worth exploring for neighbourhood restaurants.

Luxembourg's cooking leans French. It has a serious fine dining scene but thinner casual eating, and only a handful of national dishes. Its strength is Moselle Riesling and crémant by the glass, which suits a long lunch better than a food crawl.

For museums, Amsterdam is in another league. The Rijksmuseum has Rembrandt, the Van Gogh Museum has the largest collection of his work, and the Stedelijk covers modern art. Add the Anne Frank House and the UNESCO canal ring of merchant houses, and you need three or four days.

Luxembourg's draw is its setting more than its collections. The fortress walls and Bock casemates above the Alzette gorge, the view down into the Grund, and the palace and cathedral make a striking two-day visit. MUDAM on Kirchberg adds contemporary art.

Here the gap is wide. Amsterdam has a serious electronic music scene, with all-night clubs in old industrial buildings and across the IJ in Noord, and the Amsterdam Dance Event every October. For a gentler evening, there are canal-side terraces in the Jordaan and De Pijp.

Going out in Luxembourg is small-scale and busiest on Thursdays and Fridays, when the international office crowd fills the Rives de Clausen and the riverside pubs of the Grund. Hollerich stays open later, but most visitors will settle for a glass of crémant and an early night.

Luxembourg has the better landscapes. Wooded gorges run right through the middle of the city. Within half an hour, the Müllerthal has mossy sandstone ravines and beech forest along a waymarked trail, and the hills of the Ardennes and the Moselle vineyards lie further out.

Amsterdam's countryside is flat and gentle: polders, dykes and windmills in Waterland, best explored by bike after the ferry across the IJ. Closer in are the woods of the Amsterdamse Bos, and further out the bison-grazed dunes of Zuid-Kennemerland. It is pleasant, but there are no hills and little sense of wilderness.

Both are excellent bases, but Amsterdam has the richer choice. Haarlem, Leiden, Delft, Utrecht, The Hague with the Mauritshuis, and Rotterdam are all within an hour on frequent trains. Zaanse Schans and Kinderdijk have windmills, and the Keukenhof bulb fields are an easy trip in spring.

Luxembourg's strength is crossing borders. Roman Trier in Germany and Metz in France, with its Gothic cathedral, are each under an hour away. At home, Vianden's castle, Echternach and the Moselle wine villages round out a shorter but varied list.

Amsterdam has far more to fill a family week: the Artis zoo, the hands-on NEMO science museum, city farms, canal boats and pancake houses. The catch is the fast bikes and unfenced canal edges, so small children need holding on to.

Luxembourg is calm and easy with a buggy, thanks to its public lifts and funicular, and children love the casemate tunnels. Beyond the Parc Merveilleux, though, little is made for them. With no zoo or theme park, it suits a short stay of two or three days, not a school vacation.

Both are easy without a car, but in different ways. Amsterdam is flat and walkable, with trams, a metro and free ferries across the IJ. Hiring a bike is the local way to get about, if you are confident in busy cycle lanes.

In Luxembourg, all public transport is free across the whole country, so the tram to Kirchberg and the trains to Vianden or the Moselle cost nothing. The centre is built on several levels, and public lifts and a funicular take the place of the bike.

Amsterdam is the better place for shopping. The Nine Streets and the Jordaan are full of independent boutiques and vintage shops, PC Hooftstraat has the luxury labels, and De Bijenkorf is the grand department store. The markets range from the Waterlooplein flea market to the floating Bloemenmarkt.

Luxembourg's Grand-Rue serves a wealthy local clientele with premium brands, but independent design and bargains are hard to find. Villeroy & Boch porcelain and a bottle of crémant are the souvenirs to bring home.

Neither is cheap, and in both cities rooms are the biggest cost, but Amsterdam is the slightly gentler bill. Hotels on the canal ring and the tourist tax are steep. Markets, snack stalls and cycling keep daytime spending down, though, and Haarlem or Utrecht have cheaper beds.

Luxembourg is dearer still. Hotels are priced for business travellers, and meals out cost more than the Western European norm. Free transport, free museums and lunch menus help soften the bill, and many visitors sleep in Trier or Metz and come in for the day.

Amsterdam has a musical tradition of its own. The Concertgebouw and its orchestra are world famous, the national opera and ballet perform on the Amstel, the Bimhuis covers jazz, and Paradiso and the Melkweg bring in touring bands. Theatre, though, is mostly in Dutch.

Luxembourg's Philharmonie is a fine hall with its own orchestra and a good visiting programme. The Grand Théâtre often stages work in English as well as French and German, which helps visitors, but most of what plays here comes from elsewhere.

Luxembourg is the better place to slow down. Mondorf-les-Bains, half an hour away, has a warm mineral spring and a spa park that has been running since the nineteenth century. Back in the city, quiet evenings and river paths through the Grund add to the calm.

Amsterdam has no thermal tradition, though the Dutch take saunas seriously, and there are large day spas on the city's edges, mixed and nude in the Northern European way. The crowded centre works against rest, so calm comes from the quieter canals early in the morning or an afternoon in the Vondelpark.