Aarhus or Reykjavik?

Neither city is a beach destination, but Aarhus does give you a proper swim in July and August. There is fine sand at Bellevue and Den Permanente in the Risskov woods, Moesgaard Strand to the south, and calm, shallow bay water that is noticeably warmer than Reykjavik's.

Reykjavik's shore is rock, black sand and harbour wall facing a cold North Atlantic. Sea swimming there means a quick dare at Nauthólsvík followed by the hot tub, and anyone who wants to swim lengths goes to the heated outdoor pools.

Both cities cook in the New Nordic style, but Aarhus has more of it. There are several tasting-menu kitchens, neighbourhood bakeries for cardamom pastries, open sandwiches at lunch, and street-food halls for a cheaper, varied meal.

Reykjavik's strength is its ingredients: langoustine, Arctic char, lamb and skyr. A lamb soup or a hot dog by the harbour makes a good simple meal. Beyond Laugavegur and the Old Harbour the choice runs out quickly, though, and the prices lead many visitors to cook for themselves.

This is one of the widest gaps between the two cities. Aarhus has three museums of real weight: ARoS with its rainbow walkway, the open-air streets of Den Gamle By, and Moesgaard with the Grauballe Man. The Latin Quarter and the long Gothic cathedral add to them.

In Reykjavik the sights are Hallgrímskirkja, Harpa and a handful of small museums, of which the Settlement Exhibition stays with you longest. You can see all of them in a day or two. Most visitors treat the city as a base for exploring the country.

The two cities are much alike here. Both go out on Fridays and Saturdays, both are quiet midweek, and drinks are dear in both. The difference is in style: Aarhus's student-led night spreads across the riverside bars on Åboulevarden, the Latin Quarter's cellar bars and a few clubs, with wine and craft-beer bars for a slower evening.

Reykjavik's runtur packs small bars that turn into dance floors after midnight into a few blocks around Laugavegur. It starts late, runs into the early hours, and in midsummer you walk home in daylight.

Reykjavik is the clear winner, and for many visitors nature is the whole reason to go. The rift valley at Þingvellir, the Strokkur geyser and Gullfoss are all within an hour or two. Further out are glacier walks on the south coast and the steaming lava fields of Reykjanes, while whale and puffin boats leave from the Old Harbour and winter brings the northern lights.

Aarhus offers gentler country: beech woods running down to the bay, tame deer at Marselisborg, the heath hills of Mols Bjerge and canoeing on the Silkeborg lakes. It is lovely for walking and cycling, but none of it is dramatic.

From Aarhus the day trips are to towns, and trains reach most of them. You can see the Tollund Man in Silkeborg, the runestones at Jelling and Ebeltoft's cobbled old town, or go further to Odense, Ribe and Lego House in Billund.

Iceland has few towns, so outings from Reykjavik are mostly drives through the scenery. The parliament site at Þingvellir is a major historic stop. Borgarnes, Reykholt and the wooden merchant houses of Eyrarbakki are pleasant places to pause along the road rather than destinations in themselves.

Aarhus is the easier city with children. They can walk into the old shops at Den Gamle By, feed deer by hand at Marselisborg, ride the old-fashioned attractions at Tivoli Friheden and paddle at shallow summer beaches, and the bike paths are kept apart from traffic. For bigger days out, Djurs Sommerland and Legoland are within reach.

Reykjavik is safe and relaxed, and children love its pools, with slides and hot tubs, and the ice cave at Perlan. Long coach days to the waterfalls, harsh weather and the cost of feeding a family make it harder going.

Both centres are small enough to walk around. Aarhus adds wide, separated cycle lanes, buses and a light rail that reaches the beaches, Moesgaard and the coast towards Djursland, so you rarely need a car.

Reykjavik's buses are reliable but infrequent, and there is no rail of any kind. The sights most visitors come for need a hire car or a tour, and in winter wind and ice make even short walks hard work.

Aarhus has more to browse. There is a long pedestrian street of Scandinavian chains and department stores, and the Latin Quarter has independent shops selling Danish design, vintage clothes and homeware.

Reykjavik's shopping is smaller and more specialised, centred on Laugavegur and Skólavörðustígur. It is the place for a hand-knitted lopapeysa, outdoor clothing, ceramics, jewellery and homeware made from lava stone and fish leather, and Icelandic records, and the weekend flea market at the harbour adds some local colour.

Neither city is cheap, but Aarhus is noticeably easier on the budget. Meals, drinks and taxis cost Danish prices, but bakeries, the street-food halls and getting around on foot or by bike keep daily spending down.

Reykjavik is among the most expensive places anywhere. Tours, car hire and fuel come on top of already steep rooms and meals. The cheap pools, supermarkets and self-catering apartments help, but you need to budget for high costs from the start.

Aarhus has more going on. Musikhuset is home to the Aarhus Symphony Orchestra and the Danish National Opera and also hosts touring ballet and musicals. Students from the music academy feed the rock, indie and jazz venues, and the summer jazz festival and Aarhus Festuge fill the calendar in late summer.

Reykjavik has Harpa, the Iceland Symphony Orchestra and a well-known alternative and electronic scene, which is busiest during Iceland Airwaves in late autumn. Outside the festivals there is less to choose from, and in both cities most theatre is performed in the local language.

Aarhus is a good place to slow down, but nobody goes there for treatments. Its bathing habit comes from the winter swimming clubs, and on any day of the year a visitor can walk into a public sauna, sweat for a while, step down into the cold water and go back in for another round. Otherwise you unwind in the parks and over long coffee breaks, with a few hotel spas if you want a massage.

Reykjavik goes much further, because a soak is how the city ends its working day. You might swim early alongside locals, then come back after a cold day out and move from the cooler tubs to the hotter ones, chatting with whoever sits next to you while sleet falls or the sky goes dark. Know the rule before you arrive: you shower thoroughly without a swimsuit before getting in. Outside town, quieter natural hot springs along the Golden Circle let you fit a soak into a day of sightseeing.