Aarhus or Oslo?

Neither city is somewhere to plan a beach vacation. Both offer a cool summer dip rather than lazy days on the sand, but the swimming itself is different. Aarhus has proper sandy beaches on a calm, shallow bay: Bellevue, Moesgaard Strand below the woods, and the old bathing pier at Den Permanente, with wider Djursland sands under an hour away.

Oslo swims from rocks, ladders and diving platforms instead. Ferries take you to small coves on Hovedøya and Langøyene, there are swimming spots along the harbour edge at Sørenga, and the metro runs out to Sognsvann for a lake swim. The water warms slightly more there in a good July.

The two eat about equally well, and in both cities the best cooking is in Nordic tasting menus, while everyday dining is thinner and expensive. In Aarhus, look for open rye sandwiches at lunch, cardamom pastries from neighbourhood bakeries and the covered street-food halls for a cheaper, varied meal.

Oslo's edge is coffee and seafood. Light-roast cafés are everywhere, and prawns eaten on the quay are a summer ritual. Mathallen and the streets of Grünerløkka make the easiest places to wander and choose somewhere to eat.

Oslo has a little more to see, and better-known names. The Munch Museum and the National Museum hold The Scream and the core of Norwegian art, and the Bygdøy ferry leads to polar ships, Kon-Tiki and a stave church. Vigeland Park and the walkable Opera House roof are unlike anything in Denmark.

Aarhus answers with three museums of real weight: ARoS and its rainbow walkway, the townhouses of Den Gamle By, and Moesgaard with the Grauballe bog body. The Latin Quarter and the long Gothic cathedral give it a slightly older core than central Oslo. Each city fills two or three days.

Neither city is worth the trip for its nights out, but the evenings feel different. Students drive the scene in Aarhus. The busy nights are Friday and Saturday in the cellar bars of the Latin Quarter and along the river at Åboulevarden, and you can see it all in two evenings.

Oslo's going-out is more grown-up and spread wider. Grünerløkka and Youngstorget have natural wine and cocktail bars and a few electronic clubs, and the waterfront at Aker Brygge fills on long summer evenings. Drinks are even dearer, so locals start at home and go out late.

Oslo is far ahead here. The metro runs right to the edge of Nordmarka, a huge forest of lakes, trails and waffle-serving cabins. In winter it has hundreds of kilometres of ski tracks, plus downhill slopes and a toboggan run, all reachable on public transport. In summer the fjord's skerries and wooded islands are there for kayaking and sailing.

Aarhus is gentler and smaller in scale. It has beech woods running down to the bay, the Marselisborg deer park, the heathery hills of Mols Bjerge and canoeing on the Gudenå around Silkeborg. It is pleasant from spring to autumn and has little to offer outdoors in winter.

Aarhus has more and better outings. Within easy reach by train or road are the Jelling runestones, where Danish history as a nation begins, the Tollund Man at Silkeborg and Ebeltoft's cobbled streets. Lego House in Billund, Odense's Andersen sites and Ribe, Denmark's oldest town, are also possible in a day.

From Oslo, the best day out is the star-shaped fortress town of Fredrikstad, with Drøbak, Tønsberg and Lillehammer as pleasant extras. The fjord scenery Norway is famous for lies too far west for a day trip.

Aarhus works better with children, largely because of what lies around it. In town there are Den Gamle By, deer to feed in the Marselisborg woods, the small Tivoli Friheden and shallow beaches. Legoland, Djurs Sommerland and the Grenaa aquarium are all within a day trip, although a car makes them easier.

Oslo has excellent single days, such as climbing aboard the Fram, the farm animals at the Folk Museum, running up the Opera House roof and sledding near Holmenkollen. It has no big zoo, aquarium or major theme park, though, and family costs climb faster.

Oslo is the easier city to get around, because trams, metro, buses and the harbour ferries all work as one network. That network reaches the forest at Sognsvann, the fjord islands and Bygdøy, and an express train runs in from the airport. You never need a car, though winter ice makes good shoes essential.

Aarhus is smaller and flat, so walking and cycling on separated lanes cover most of it, with buses and the light rail for the beaches and Moesgaard. You only need to hire a car for the scattered manors and theme parks in the countryside.

The shopping is on a similar scale, so it comes down to what you want to buy. Aarhus is best for Danish design. Beyond the chain stores on its long pedestrian street, small shops in the Latin Quarter sell ceramics, lighting and clean-lined clothing.

Oslo goes slightly further upmarket, with the old Steen & Strøm department store and Bogstadveien. The things to take home there are Norwegian: patterned knitwear, outdoor clothing and silver, with vintage and records in Grünerløkka.

Both are expensive, but Aarhus is noticeably easier on the wallet. Its hotels cost less, and its bakeries and street-food halls make cheap, filling meals. The centre is small enough that you rarely pay for transport.

Oslo costs more at almost every turn, and alcohol in particular. What saves money there is free things: Vigeland Park, the Opera House roof, the forest trails, and harbour ferries covered by an ordinary transport pass.

Oslo has the stronger stage. A night of opera or ballet in the oak-lined hall of the harbour Opera House is a highlight in itself, and the Oslo Philharmonic and the August festival in Tøyen park add weight. Ibsen at the National Theatre is mostly in Norwegian.

Aarhus has a capable but smaller calendar centred on Musikhuset, home to the symphony orchestra and the Danish National Opera. Students from the music academy keep the rock, indie and jazz venues going. Its busiest weeks are the summer jazz festival and Festuge in late summer.

Both cities relax the Nordic way, with a hot sauna and a cold plunge, and neither has thermal springs. In Oslo the habit is more central and easier to join. Floating wood-fired saunas line the harbour by the Opera House and at Sørenga, and people climb down into the fjord all year round.

Aarhus has the same idea on a smaller scale, with harbour saunas, Den Permanente and its winter swimming clubs. Beyond those, its calm parks and slow coffee breaks are most of what it offers for unwinding.