Oslo or Reykjavik?

Neither city is a beach destination, but Oslo at least has a swimming season. In July the fjord is calm and warm enough for a proper swim, and ferries take you to the rocky coves of Hovedøya and Langøyene, or you can swim off the platforms at Sørenga or in the forest lake at Sognsvann.

Reykjavik's North Atlantic barely gets past 12°C, and its shore is mostly rock and black sand. The one beach worth visiting is Nauthólsvík, where geothermal water warms a small lagoon, and otherwise swimming means the heated outdoor pools.

Both kitchens rely on cold-water fish, lamb or game and Nordic restraint, but Oslo has more depth. It has a solid tier of tasting menus, a food hall at Mathallen, the restaurant streets of Grünerløkka and a specialty coffee culture good enough to plan your mornings around.

Reykjavik is good for simple, honest food: lamb soup, plokkfiskur and harbour-side hot dogs. Beyond the few streets around Laugavegur and the Old Harbour, though, the choice soon runs thin. In both cities eating out is costly enough that supermarket meals are part of the plan.

Oslo gives you far more to see. The Munch Museum and the National Museum hold the great Norwegian art, Bygdøy has the Fram and Kon-Tiki museums and an open-air folk museum with a stave church, and Akershus Fortress, City Hall and the walkable Opera House roof fill out the centre. That makes two or three full days of sightseeing.

Reykjavik's list is short: Hallgrímskirkja and its tower view, Harpa, the Sun Voyager and a handful of small museums, of which the Viking-age longhouse in the Settlement Exhibition is the most memorable. A stroll past the corrugated-iron houses around Tjörnin rounds off a day, and then most visitors head out of town.

The two are broadly level, and both are held back by heavily taxed alcohol and the local habit of drinking at home before going out. What differs is the shape of a night. Oslo spreads its going out across Grünerløkka, Youngstorget and Grønland, with natural wine bars, craft beer and a few electronic clubs, plus outdoor drinking on the Aker Brygge waterfront in summer.

Reykjavik packs everything into a few blocks and saves its energy for Friday and Saturday, when the runtur crawl turns small bars into dance floors until the early hours. In midsummer you leave the last bar into daylight.

Reykjavik has the more spectacular landscape. Þingvellir's rift valley, the Strokkur geyser, Gullfoss, the south-coast waterfalls and the glacier at Sólheimajökull are all within reach, and Reykjanes adds lava fields and steaming mud pools close to the airport. Whale and puffin boats leave from the Old Harbour, and winter brings ice caves and the northern lights.

Oslo's countryside is gentler but much easier to reach. The metro climbs straight into the Nordmarka forest, which has lakes and trails in summer and floodlit ski tracks in winter, and ferries cross to the fjord islands for kayaking and coastal walks. You do not need a car, but there are no volcanoes or glaciers either.

Oslo has the better choice of towns for a day out, and a train gets you to most of them. Fredrikstad's star-shaped fortress is about an hour south, Drøbak's white wooden houses are a summer boat ride down the fjord, and Lillehammer offers an open-air museum and Olympic ski jumps.

From Reykjavik, the outings are historic stops on a scenic drive rather than places in their own right. The exception is Þingvellir, where Iceland's parliament met in the open air from 930. Skálholt, Snorri Sturluson's Reykholt and the merchant houses of Eyrarbakki round out a day on the road.

Oslo has more to fill a family vacation. Children can climb aboard the polar ship at the Fram Museum, meet farm animals at the Folk Museum and try the hands-on science museum, and the amusement park at Tusenfryd is a short bus ride away. Pram-friendly trams and ferries make every outing easy.

Reykjavik is just as safe and relaxed, and its outdoor pools with slides and hot tubs are a daily treat children love. Perlan's ice cave and the whale boats add more, but bigger outings mean long coach days in uncertain weather.

Oslo is much easier to get around. Its centre is walkable from the Royal Palace to the harbour, and a single network of trams, metro, buses and ferries reaches the forest hills and fjord islands. An express train runs from the airport, so you never need a car.

In Reykjavik you can walk across the centre in half an hour, but the buses are not frequent and there is no rail of any kind. Leaving the city means a coach, a tour or a hire car, and in winter wind and ice make even short walks harder.

Oslo has the wider range. Karl Johans gate has the chains, the historic Steen & Strøm department store gathers Nordic and luxury brands, Bogstadveien is where locals shop, and Grünerløkka adds vintage and design.

Reykjavik's shopping fits into Laugavegur and Skólavörðustígur, and it is worth a visit mainly for the hand-knitted lopapeysa, lava-stone and fish-leather design, and local records. There are no department stores, and the weekend harbour flea market is the only real browse.

Both are among the dearest places you can visit, and neither rewards a tight budget. Oslo is the slightly easier of the two: Vigeland Park, the Opera House roof, the forest trails and the fjord islands are free, and one transport pass covers the harbour ferries.

In Reykjavik, even a simple guesthouse or a plain meal costs a lot, and the trips most people come for depend on paid tours or car hire and fuel. The cheap geothermal pools, superb tap water and self-catering apartments are what keep a budget under control.

Oslo has more on stage. The Opera House is home to the national opera and ballet, the Oslo Philharmonic plays at the Konserthus, and the National Theatre stages Ibsen in his own city. Small jazz and rock clubs and a big August festival in Tøyen park fill out the year.

Reykjavik punches above its size, with the Iceland Symphony Orchestra at Harpa, but its strength lies in alternative and electronic music in small bars. Time a trip for Iceland Airwaves in late autumn and the city comes alive with music. At other times the choice is thin.

Reykjavik is the place to unwind. Every district has a geothermal outdoor pool with hot tubs at different temperatures, a cold plunge and a steam room, and soaking at Vesturbæjarlaug or Laugardalslaug with the locals is the heart of the city's daily life. The Blue Lagoon and quieter springs along the Golden Circle lie further out.

Oslo's version is the wood-fired sauna, many of them floating by the Opera House and at Sørenga, followed by a climb down into the fjord. It is sociable and easy to join, but there is no hot water from the ground and few spa hotels.