Budapest or Wroclaw?

Neither city is a beach destination, but Budapest gives a swimmer far more to work with. Its summer lidos, with lawns and several pools, fill a whole day. The shallow, warm water of Lake Velence is under an hour away by train, and Balaton can be reached for a long day out.

Wroclaw's sandy Oder beaches are for deckchairs and a drink rather than a swim, so getting in the water means a public pool or a drive to a lake in the countryside. The Baltic is too far for anything but a separate trip.

Budapest is the stronger place to eat. Paprika-red goulash, fisherman's soup and lángos, the salami and dried peppers of the Great Market Hall, and the layered cakes of the old coffee houses make eating part of the sightseeing. Hungarian wine from Tokaj, Eger and Balaton is a real find.

Wroclaw feeds you well rather than memorably, with pierogi, żurek in a bread bowl, roast duck, cheap milk-bar lunches and a few modern Polish bistros. Its drinking leans towards beer in cellar brewpubs and craft taps rather than wine.

Budapest has the grander set piece. Parliament faces the Royal Palace and the Fishermen's Bastion across the Danube, Andrássy Avenue runs out to Heroes' Square, and the Museum of Fine Arts and the National Gallery hold serious collections. Add the Dohány Street Synagogue, the Art Nouveau buildings and Memento Park, and the city fills several days.

Wroclaw's sights are smaller in scale and quicker to see. They centre on the vast Market Square with its Gothic Town Hall, the brick churches of Ostrów Tumski and the concrete Centennial Hall. Its post-war rebuilding and the Racławice Panorama give it a story of its own, and the bronze dwarfs add a playful hunt.

Budapest's nights are bigger and go on later. The ruin bars of District VII fill whole tenement courtyards, Kazinczy and Király streets add late clubs, and summer brings party boats and terraces along the Danube, though the centre can turn rowdy at weekends.

Wroclaw's night out is lively for its size but depends on its students. People drift between bars in the Ruska Street courtyard passage and the cellars around the Market Square, and the club scene is modest. Things go quieter between university terms.

The outdoors is close to even here, but it takes a different shape. Budapest has forested hills inside the city. The Buda Hills are reached by cogwheel railway and chairlift, with thermal caves beneath, and the ridges and riverside cycle path of the Danube Bend are an hour north. It is all gentle walking.

Wroclaw is flat, and its green space comes from the river islands, Szczytnicki Park and the botanical garden. For height you head further out, to the lone peak of Ślęża or, about two hours away, the Karkonosze and the sandstone Table Mountains, which offer proper hiking and winter skiing that Budapest lacks.

Budapest has the easier and richer choice of outings. Szentendre, Visegrád and Esztergom line the Danube Bend within reach of a suburban train, and Gödöllő's palace is a half-day. At around two hours, Eger's castle and wine cellars and the village of Hollókő widen the choice.

Lower Silesia has plenty of castles and churches, and the highlights are Książ above its wooded gorge and the wooden Churches of Peace. A car makes the difference there, because combining several stops in a day by train is awkward.

Both cities work well with children, in different ways. Budapest has more to fill the days, from the City Park zoo and the Children's Railway to summer lidos with wave pools, but metro stairs and loud weekends in District VII need some planning.

Wroclaw is the calmer base, flat and largely car-free around the Market Square, and its big draws are the dwarf hunt and the shark tunnel in the zoo's Afrykarium. Once those are done, the list runs short.

Budapest is easier to get around. Central Pest is flat and walkable, trams circle the Grand Boulevard round the clock, and tram 2 doubles as a sightseeing ride along the river. The short metro, the ferries and cheap taxis cover the rest, including hilly Buda.

Wroclaw's centre is compact and largely pedestrianised, so walking does most of the work, and bikes are popular along the river. Further out the trams are slow at rush hour, and the countryside sights are easier by car.

Budapest gives a shopper more to do, though not a great deal. Herend and Zsolnay porcelain, Hungarian design boutiques in Districts V and VII, a few luxury labels on Andrássy Avenue and the Ecseri flea market are better hunting than the souvenir shops of Váci utca.

Wroclaw is mostly malls and chains, though the 1930s Renoma building is worth a look for its ceramic facade. The buys to look for are Bolesławiec stoneware, amber and the vintage finds of Nadodrze.

Wroclaw is the cheaper stay. Central hotels, milk-bar lunches, beer, trams and museums all cost little, and only the Market Square terraces and busy summer weekends push prices up.

Budapest is still good value beside Western capitals, with cheap transport and wine, but it costs more overall, and the streets around Váci utca and the Basilica charge extra. Eating set lunch menus in residential districts narrows the gap.

Budapest is the stronger music city. With the State Opera House on Andrássy Avenue, the Art Nouveau hall of the Liszt Academy and the national concert hall at Müpa, there is classical music most nights, and operetta and the folk ensembles add something local.

Wroclaw has a respectable programme for its size: the National Forum of Music, the opera house near the moat, and festivals such as Wratislavia Cantans and Jazz on the Oder. In both cities spoken theatre is in the local language, so visitors come for the music.

This is where the two cities are furthest apart. Budapest sits on more than a hundred hot springs, and an afternoon moving between the pools of the Széchenyi, the mosaics of the Gellért or the Ottoman domes of Rudas and Király is a reason to come in itself.

Wroclaw has no bathing tradition of its own, only hotel spas and an indoor aquapark with saunas. To take the waters you travel an hour or more to the old spa towns of Lower Silesia, such as Szczawno-Zdrój.