Lima or Mexico City?

Neither city is built around the beach, but only Lima has a coast at all. Below the Miraflores cliffs, the Costa Verde is grey pebble with steady surf, better for surfing than swimming. The sandy beaches at Punta Hermosa and San Bartolo, about an hour south, make a good summer day out.

Mexico City sits on its high plateau with Acapulco several hours away, so swimming there means a hotel pool. If you want to see the sea, Lima offers it every day. From Mexico City it means adding separate days on the coast.

Both cities are among the great places to eat in the Americas, and both have celebrated tasting menus. What differs is the cooking itself. Lima is a seafood city: ceviche and tiradito at lunchtime cevicherías, Nikkei raw fish, Chinese-Peruvian chifa, and anticuchos grilled on street carts in the evening, with pisco sours to drink.

Mexico City eats from the street at every hour: al pastor tacos late at night, tamales and atole at breakfast, blue-corn quesadillas at market counters in Medellín or La Merced. Mezcal and pulque are the drinks. The best places are spread across a vast city, while Lima's cluster more closely around Miraflores.

Lima has plenty for two or three good days: the UNESCO-listed viceregal centre with its carved wooden balconies, the catacombs of San Francisco, pre-Columbian gold at the Larco Museum and the adobe pyramid of Huaca Pucllana among the Miraflores apartment blocks.

Mexico City works on a different scale. The Templo Mayor's excavated Aztec ruins sit beside the cathedral on the Zócalo, Rivera's murals cover the National Palace stairwell, and the Anthropology Museum alone fills a day. Then there are Coyoacán, San Ángel and Xochimilco, which is why a week there still feels short.

Lima's nights centre on Barranco, where bars and clubs in old mansions fill from midnight and dance to salsa, cumbia and reggaetón until dawn at weekends. On weeknights it's much quieter.

Mexico City offers more and a wider range. In Roma and Condesa you can walk between cocktail bars, mezcalerías and rooftops along tree-lined streets. There are old cantinas in the Centro, electronic clubs that run until morning, salsa halls and a large LGBTQ scene in the Zona Rosa. In both cities, take a car home late at night.

The outdoors is about equal in the two cities but completely different in character. Lima faces the ocean: you walk or cycle the clifftop malecón, watch the paragliders, surf all year and swim among sea lions at the Palomino Islands. Inland, though, the desert hills stay brown for most of the year.

Mexico City looks to the mountains, with pine-forest hiking at Desierto de los Leones and Ajusco and the volcano pass between Iztaccíhuatl and Popocatépetl about two hours out. The traffic on the way out and poor air in the dry season take some of the pleasure away.

Lima's day trips are thin. Pachacamac's adobe temples and the old port of Callao fill a day or two. Caral and Paracas are far enough away to need an overnight stay.

Mexico City is one of the best bases in the Americas for day trips. Teotihuacan's pyramids are an hour away, Puebla and the great pyramid at Cholula about two. To the south lie Tepoztlán, Cuernavaca and the silver town of Taxco, so a longer stay can easily include several outings beyond the city.

Both cultures welcome children warmly, and both cities have tiring traffic. Lima's best family days are Parque de las Leyendas, with its zoo and ruins, the evening fountains of the Circuito Mágico del Agua and, in summer, the southern beaches.

Mexico City gives families more to fill a week. Chapultepec has the zoo, boating lakes and the hands-on Papalote museum, and there's an aquarium, a roller-coaster park, trajinera boats at Xochimilco and lucha libre. Allow a slow first day while everyone adjusts to the altitude.

In Lima, the clifftop path between Miraflores and Barranco is pleasant on foot, but beyond those two districts nearly every journey is a taxi or ride-hailing car stuck in some of South America's slowest traffic. Only the Metropolitano bus lanes reliably cut through to the historic centre.

Mexico City is larger but easier to move around. The cheap metro, with its pictogram stations, the Metrobús and bike-share link walkable areas such as Roma, Condesa and Coyoacán. Trains are packed at rush hour and pickpockets work them, so keep an eye on your bags.

Lima's shopping comes down to Peruvian materials: baby alpaca knitwear in Miraflores and San Isidro, regional crafts along Avenida Petit Thouars, and a few designer shops in Barranco. Beyond that it's mostly malls.

Mexico City gives a shopper much more ground to cover. La Ciudadela gathers pottery, alebrijes and silver from across Mexico, San Ángel's Saturday bazaar and the Sunday flea market at La Lagunilla make for long browsing, and Avenida Presidente Masaryk adds the luxury brands Lima lacks.

Both are cheap to live in day to day, and in both the cost rises sharply at the top. In Lima, what drives a budget up is dining: set lunch menus cost little, but the famous tasting menus and smart Miraflores cevicherías charge international prices.

In Mexico City, the big cost is where you stay. Boutique hotels in Roma, Condesa and Polanco charge close to European prices, while tacos, market lunches and the metro stay very cheap. Staying in the Centro instead saves a good deal.

Lima's best night out on stage is a peña in Barranco, with música criolla and Afro-Peruvian cajón where the audience ends up dancing. The concert halls play a smaller part.

Mexico City has more on stage. The Ballet Folklórico at Bellas Artes works even if you speak no Spanish, the university orchestra plays in its modernist hall, mariachis fill Plaza Garibaldi every night, and lucha libre at Arena México is a show in itself.

Neither city is restful. Lima has no bathing tradition, and relaxation there means a hotel spa or an early walk in the clifftop parks.

Mexico City has more to offer, mainly the pre-Hispanic temazcal steam bath, along with shaded plazas in Coyoacán. Its real advantage is the warm towns of Cuernavaca and Tepoztlán close by, where spas are part of local life.