Cusco or Mexico City?

Neither city works for a beach trip. Both are high inland cities, and swimming means a hotel pool at best. The difference is how far the sea is. From Cusco the Pacific coast means a flight, and the lagoons in the hills are glacial. From Mexico City you can drive to Acapulco in several hours, so a few days on the coast are easier to add before or after.

Mexico City is one of the great eating cities, and Cusco can't match its range. In Mexico City, al pastor and blue corn quesadillas from street stands, markets such as Medellín and La Merced, cantinas, pulquerías and serious tasting menus in Roma, Condesa and Polanco make food a reason to go in itself.

Cusco cooks well within a narrower range: highland potatoes and maize, trout, alpaca, cuy and slow-cooked dishes from the picanterías, with Novoandino tasting menus in San Blas. Once you step away from Peruvian food the choice thins out, and the menus around the Plaza de Armas are mostly aimed at tour groups.

Both cities stand on a conquered capital, but you see it in different ways. In Cusco the Inca city is still part of the streets. You walk past mortarless walls such as Hatun Rumiyoc, see Qorikancha under the Santo Domingo monastery, and climb to the zigzag ramparts of Sacsayhuamán. The museums are worthwhile but small.

Mexico City has more, and on a bigger scale. The Templo Mayor sits beside the cathedral and National Palace with Rivera's murals, the Anthropology Museum is one of the world's great archaeological collections, and there are the Kahlo and Rivera houses in Coyoacán and San Ángel. A week barely covers it, while Cusco's sights fit into a few days.

After dark, the gap between the two is wide. Mexico City goes out late and stays out, from walks between cocktail bars and mezcalerías in Roma and Condesa to old cantinas in the Centro, electronic clubs that run until morning, salsa halls full of locals, and the LGBTQ scene of the Zona Rosa.

In Cusco, going out means a few bars and clubs off the Plaza de Armas, filled with backpackers and pub crawls, plus some quieter bars in San Blas. Altitude and pre-dawn tour departures mean most visitors keep their evenings short.

This is Cusco's strongest point. The Sacred Valley lies just below the city under the snow peaks of the Cordillera Urubamba, and from here you can walk the Inca Trail, Salkantay or the Ausangate circuit, hike to Rainbow Mountain at over 5,000m, raft the Apurímac or spot vicuñas on the high grassland.

Mexico City has Chapultepec, the Xochimilco wetlands and pine forest on Ajusco, and the Iztaccíhuatl and Popocatépetl volcanoes and the Nevado de Toluca crater lakes about two hours out. Traffic eats into those days, though, and the air can be poor in the dry season.

Both are very good bases for day trips, but in different ways. From Cusco nearly every outing is Inca or colonial: Pisac, Ollantaytambo, Chinchero, Moray and the Maras salt pans in the Sacred Valley. Machu Picchu is the highlight, but between the road, the train and the bus it makes a very long day, so many people stay a night instead.

Mexico City offers more variety. Teotihuacan's pyramids are about an hour away, Puebla and Cholula have tiled churches and their own cooking, and there is warm, green Cuernavaca, the cliff-top temple at Tepoztlán and the silver town of Taxco. The price of that variety is getting out through the city's traffic.

Mexico City is much the better place for children. Chapultepec has the zoo, boating lakes and the hands-on Papalote museum, and there is an aquarium, a theme park, the Xochimilco boats and lucha libre, in a culture that welcomes children in restaurants. The main problems are distance and traffic.

Cusco is hard with small children. At 3,400m altitude sickness is a real risk, the pavements are narrow and steep, and the days are full of ruins, churches and early starts. Older children who like history do well there, and families often stay lower down in the Sacred Valley among the llamas.

Getting around is about equally manageable in both, but for opposite reasons. Cusco's centre is small enough to walk from the Plaza de Armas, but the climbs to San Blas and Sacsayhuamán are tiring in thin air, there is no metro, and cheap taxis handle the uphill trips home.

Mexico City is huge. You walk within the Centro, Roma, Condesa or Coyoacán and use the cheap metro, the Metrobús, bike-share or ride-hailing between them. The metro is crowded at rush hour, so watch for pickpockets.

In Cusco shopping comes down to Andean textiles: alpaca knitwear, ponchos and naturally dyed weaving from cooperatives such as Chinchero's, plus ceramics and silver from San Blas. Much of the stock around the square is factory-made, and there is almost no fashion.

Mexico City brings crafts from the whole country together in La Ciudadela, and adds San Ángel's Saturday art bazaar, antiques at La Lagunilla, luxury houses on Masaryk in Polanco and Mexican designers in Roma and Condesa. That makes it the better place for a shopping trip.

Both are cheap day to day, with low-cost market lunches and taxis or rides, but the large expenses come in different places. In Cusco the train and entry for Machu Picchu and guided treks such as the Inca Trail are hard to avoid, and they take up much of the budget. In Mexico City you control the big cost yourself: stay and drink outside Roma, Condesa and Polanco, and the city stays inexpensive.

Mexico City has a full calendar of performance. Bellas Artes hosts the national opera, the symphony and the Ballet Folklórico, there are concerts at Sala Nezahualcóyotl and the Auditorio Nacional, jazz and son clubs, mariachis in Plaza Garibaldi and lucha libre at Arena México.

Cusco's evenings mostly offer folkloric shows and panpipe bands over dinner. Its real strength is its festivals, with Inti Raymi at Sacsayhuamán around the June solstice and the masked dancers of Corpus Christi and Qoyllur Rit'i.

Neither city is restful, and from both of them people go to lower towns to relax. Mexico City does a little better. It has the temazcal, a pre-Hispanic steam bath, good spas in Polanco and Condesa, and quiet plazas in Coyoacán, with Cuernavaca and Tepoztlán close by for a proper retreat.

In Cusco, cheap street massage and hotels that pump oxygen into rooms help with the altitude. For real calm, though, you head down to the riverside lodges of the Sacred Valley, and the nearest hot springs are well outside the city.