Amsterdam or Cologne?

Neither city is a beach destination, but Amsterdam at least has a real sandy shore within reach. Zandvoort and Bloemendaal are about half an hour away by train, with dunes and summer beach pavilions, though the cold, windy North Sea means most people walk rather than swim. In the city, IJburg's man-made beaches and the Sloterplas cover hot days.

Cologne has no coast within a day out, and the Rhine is too fast and busy for bathing. Its swimming is in the gravel-pit lakes on the city's edge, such as Fühlinger See and Otto-Maigler-See, where the water is often warmer than the North Sea, but they are an afternoon off rather than a reason to come.

The two are close, with Amsterdam a little ahead on range. Its best eating comes from its trading past: Indonesian rijsttafel, Surinamese roti, herring from street stalls, and the borrel of beer and bitterballen in old brown cafés and jenever tasting rooms. De Pijp, the Jordaan and Oost reward exploring.

Cologne's food is built around one ritual, the Brauhaus, where Köbes keep the small glasses of Kölsch coming alongside Himmel un Ääd and sauerbraten. Beyond that the strongest eating is Turkish and Middle Eastern along Ehrenfeld's Venloer Strasse, so it is more of a drinking-culture city than a food one.

Amsterdam is the stronger cultural trip. The Rijksmuseum's Dutch masters, the Van Gogh collection and the Anne Frank House are among Europe's essential visits, and the 17th-century canal ring means the streets between them are a sight too.

Cologne has the single most striking building of the two in its cathedral, with the Shrine of the Three Kings, plus twelve Romanesque churches, Roman remains and Museum Ludwig's Pop Art. But the city was rebuilt quickly after the war, so you go from one great building to the next through plain streets, whereas Amsterdam holds together as a historic whole.

Amsterdam has the bigger reputation, above all for electronic music. Clubs with all-night licences in old industrial buildings, many across the IJ in Noord, and the Amsterdam Dance Event each October draw clubbers from abroad, while the Jordaan and De Pijp suit canal-side drinking.

Cologne goes out in a more unpretentious, local way: from the Altstadt brewhouses to Belgian Quarter cocktail bars, the student crowd on Zülpicher Strasse and Ehrenfeld's factory clubs, with one of Germany's largest gay scenes around Rudolfplatz. Its great moment is Carnival, when the whole city parties in costume for days, but on an ordinary weeknight it is quieter.

Cologne has the better outdoors. Within about forty minutes the land rises into the Siebengebirge, with the Drachenfels crag and marked trails above the Rhine, and the Eifel's crater lakes and the Ahr valley vineyards are about an hour away. The Grüngürtel parks and long Rhine cycle paths cover the city itself.

Amsterdam's countryside is flat and gentle: polders, dykes and windmills best seen by bike in Waterland, a short ferry ride from the centre. The Amsterdamse Bos and the bison-grazed dunes of Zuid-Kennemerland add variety, but there are no hills at all.

Both make excellent bases, with Amsterdam slightly ahead because so many historic towns lie so close. Haarlem is barely a quarter of an hour away, and Leiden, Delft, Utrecht, The Hague's Mauritshuis, Kinderdijk's windmills and the Keukenhof in spring are all easy outings by train.

Cologne's day trips are more varied in kind: the rococo palaces at Brühl, Beethoven's birthplace in Bonn, Charlemagne's chapel in Aachen and, about an hour and a half south, the castle-topped wine towns of the Rhine Gorge. Crossing borders is easy too, with Maastricht, Liège and Brussels in reach.

Both are easy with children, and the difference is in the attractions. Amsterdam has the Artis zoo, NEMO's hands-on science and canal boat trips, but fast bikes, unfenced canal edges and steep canal-house stairs mean small children need watching.

Cologne's Chocolate Museum, the cable car over the Rhine and traffic-free riverside promenades are an easy fit for children, and Phantasialand, one of Europe's major theme parks, is a short trip south, much closer than Efteling is to Amsterdam. Just avoid Carnival with small children.

Amsterdam is easier to get around. Almost everything lies within half an hour's walk across a flat centre, trams and a metro fill the gaps, free ferries cross the IJ, and Schiphol is a short direct train ride away. Hiring a bike is the natural way to move, provided you can handle busy lanes.

Cologne is simple for the core sights, since the main station sits beside the cathedral and the Altstadt and river are walkable. Getting further out to Ehrenfeld or the zoo means the trams and Stadtbahn, whose map is less intuitive and whose services can be crowded and irregular.

Amsterdam is the better place to browse. The Nine Streets and the Jordaan are full of independent boutiques and vintage shops, PC Hooftstraat has the luxury labels, and markets such as the Albert Cuyp, Noordermarkt and the floating Bloemenmarkt add character.

Cologne is more of a high-street city, with Schildergasse and Hohe Strasse full of chain and department stores, while Ehrenstrasse and the Belgian Quarter hold its independents. Its distinctive buys are Eau de Cologne from the historic Glockengasse perfume houses, and its Advent Christmas markets are the big seasonal draw.

Cologne is clearly the cheaper stay. Hotels are moderate in ordinary weeks, brewhouse meals cost less than in most capitals, and the cathedral and many churches are free. The catch is that rates jump during the big Messe trade fairs and Carnival, so check dates before booking.

Amsterdam is expensive above all for rooms, which around the canal ring are among Europe's costliest, with a substantial tourist tax on top and museum tickets that add up. Staying in Haarlem or Utrecht and leaning on markets and snack stalls helps.

Amsterdam has the edge, thanks largely to the Concertgebouw and its orchestra, with the Dutch National Opera and Ballet on the Amstel, the Bimhuis for jazz, and Paradiso and the Melkweg for touring bands. Theatre is mostly in Dutch, and the Holland Festival brings international work each June.

Cologne offers a broad, solid programme of its own: the Philharmonie beside the cathedral with two orchestras, the opera and Schauspiel, early music in the Romanesque churches and small gig venues in Ehrenfeld and the Südstadt. The Carnival sessions with their dialect bands are something Amsterdam has no equivalent for.

Only one of these cities has hot springs, and that puts Cologne ahead for a restful stay. Both take saunas seriously, but Amsterdam has no bathing tradition beyond that, just large day spas on the city's edges and hotel spas. Calm there comes from an early walk along the quieter canals or an afternoon in the Vondelpark, away from a centre crowded with visitors and bikes.

Cologne has a thermal bath in the Rheinpark, fed by local mineral springs and looking back across the river to the cathedral, and locals treat its big sauna landscapes as an ordinary weekend habit. Aachen, where people have bathed in the hot springs since Roman times, is under forty minutes by train. Just avoid Carnival if rest is the point of the trip.