Page, Arizona or Palm Springs?

Neither town is on the sea, but Page has real open-water swimming. In summer Lake Powell warms enough for long swims, and Lone Rock Beach has sand you can drive onto. Boats reach sandstone coves where you jump off the rock into deep water. There are no lifeguards, though, and the shoreline moves with the lake level.

In Palm Springs, swimming means the hotel pool. That is pleasant for lounging but no substitute for a lake, and the ocean is a long drive away over the mountains.

Eating out is more of a pleasure in Palm Springs. It has long brunches on shaded patios, cocktails by the pool, date shakes from the groves around Indio and honest taquerias in the towns further down the valley.

In Page you mostly refuel between outings at diners and barbecue places. The Navajo taco on frybread is the one dish worth looking for. Neither town has much fine dining, but Page also shuts early.

Palm Springs has a real sight in its mid-century architecture: Albert Frey's angular houses, Neutra's Kaufmann House and the folded roofs of the Alexander homes in Twin Palms. Add an art museum and the Agua Caliente Cultural Museum on Cahuilla history and you have a full day or two.

Page was founded in the 1950s for the dam builders and has little beyond the Carl Hayden Visitor Center at Glen Canyon Dam and a small John Wesley Powell museum. Its deeper culture belongs to the surrounding Navajo Nation, not to anything in town.

Palm Springs at least offers a night out. There are the LGBTQ bars and drag nights around Arenas Road, retro cocktail lounges on Palm Canyon Drive and pool parties at weekends in spring, even if few places stay open into the small hours.

Page has a brewpub and a handful of bars, and most visitors go to bed early for a sunrise canyon tour. Its best evening is looking up at the dark desert sky.

Both towns sit in remarkable desert country, but Page's surroundings are in a class of their own. Within reach are the glowing slot canyons of Antelope Canyon, the river loop at Horseshoe Bend, the flooded red canyons of Lake Powell, Rainbow Bridge, rafting from Lees Ferry and the Wave in the Vermilion Cliffs.

Palm Springs offers contrast rather than grandeur. You can ride the tramway from the desert floor up to pine forest on Mount San Jacinto, walk to palm oases in the Indian Canyons and drive an hour to Joshua Tree. In summer its heat cuts hiking back to the early morning, whereas in Page the summer simply moves out onto the water.

Palm Springs has the more varied outings, all small and full of character: the mountain village of Idyllwild, the lived-in film set of Pioneertown, Salvation Mountain by the Salton Sea and the wineries of Temecula.

From Page the towns and heritage sites worth a day are few and far apart. They include the pioneer buildings at Lees Ferry, the cliff dwellings of Navajo National Monument and the Western town of Kanab, with long empty drives in between.

The two are about equal for families, in different ways, and neither is ideal. Page suits children who love being outside: splashing at Lone Rock, a boat on the lake and short Antelope Canyon tours. The drawbacks are unfenced cliff edges, steep ladders on some tours and long days in the car.

Palm Springs has more made for children, with the Living Desert zoo, the tramway and the Air Museum. Many of its boutique hotels are adults-only, though, so families do better in the larger resorts down the valley.

You need a car in both, but Palm Springs asks a little less of it. Its downtown is flat and easy to walk, bikes work well for the mid-century neighbourhoods in the cooler months, slow valley buses run between the towns, and the airport is on the edge of town.

Page has a walkable motel strip and little else. The sights, the marinas and the nearest major airports are all a drive away, which is why most visitors arrive on a road trip.

Palm Springs is a proper shopping stop. Mid-century furniture, lighting and vintage clothing fill the Uptown Design District, with El Paseo in Palm Desert and the Cabazon outlets for everything else.

Page sells supplies and souvenirs, with one exception Palm Springs cannot match: Navajo silver, turquoise, rugs and pottery, bought at trading posts or straight from the makers.

Neither town is cheap, but the ways to save are different. In Page the costs come from scarce rooms in the busy months, paid Antelope Canyon tours and boat hire. Camping at Lone Rock or Wahweap, or coming in winter, brings them down.

Palm Springs is most expensive in its winter and spring high season, especially on festival weekends. In the scorching summer it becomes a bargain, when room rates fall sharply.

Palm Springs has a calendar worth checking. Coachella and Stagecoach come to Indio each April, the McCallum Theatre hosts touring shows, the casinos book concerts, and drag cabaret and piano bars fill evenings in town, though most of it stops in summer.

Page has almost nothing to plan around, beyond Navajo dance presentations staged for visitors and the occasional band in a bar.

Palm Springs is far ahead here. The town grew up around the Agua Caliente hot spring, whose bathhouse lets you soak in its mineral water. Nearby, the spa motels of Desert Hot Springs fill their pools straight from the ground, and there are resort spas across the valley.

Page has motel pools and quiet evenings with wide views. Its days start before dawn and revolve around long drives, though, so it suits an active trip far more than a restful one.