Los Angeles or Page, Arizona?

The two are close here, but the water is very different. Los Angeles has more than 100km of real coastline, from Zuma and El Matador to the South Bay. There you get volleyball, surf breaks and boardwalks, but the Pacific is cold enough that most people wade or wear a wetsuit.

Page has no coast at all, but in summer Lake Powell is far warmer for swimming. Days there are spent jumping off sandstone into deep coves from a boat, or driving down onto the sand at Lone Rock. There are no lifeguards and no beach town, and the shoreline moves as the lake rises and falls.

This is one of the widest gaps between the two. Los Angeles is a reason to travel in its own right. Its immigrant communities cook at full strength, from Thai Town and Little Ethiopia to the Oaxacan kitchens of Mid-City, and on top of that come serious chef-led restaurants, coffee culture and year-round farmers' markets.

Page feeds road-trippers and tour groups with diners, barbecue and chains. The Navajo taco is the one dish worth looking for. There is no market or fine-dining scene, so in Page food is simply fuel between outings.

Los Angeles gives a culture trip a great deal to work with: the Getty Center and Villa, LACMA and the Broad, the Huntington's library and gardens, and Hollywood's movie palaces and studio lots. It has little old city, but the art and architecture are deep.

Page was only founded in the 1950s, as a town for the dam workers. Its sights are the Glen Canyon Dam visitor centre and a small museum about John Wesley Powell. The cultural depth of the area comes from the surrounding Navajo Nation rather than from anything indoors.

Los Angeles offers a real choice of nights out: velvet-rope clubs in Hollywood, the gay strip on Santa Monica Boulevard, dive bars in Echo Park and loose beach-town crowds in Venice. Bars close at 2am and getting between districts takes a ride, but the range is huge.

In Page there are a few bars and a brewpub, and the town is quiet well before midnight. Most visitors are in bed early for the canyon tours. The best thing to do after dark is look up at a sky full of stars.

Los Angeles has more wild country close by than most big cities: trails in Griffith Park, the Santa Monica Mountains running down to the sea, the San Gabriels above 3,000m and boats out to the Channel Islands. Its problem is the traffic between you and all of it.

Page comes out ahead because the landscape starts at the edge of town. You can see the glowing walls of Antelope Canyon and the river loop at Horseshoe Bend, explore Lake Powell's flooded red canyons by houseboat or kayak, and reach the Wave and Buckskin Gulch within a couple of hours. Here the landscape is the main reason to come, not something to fit in between other things.

From Los Angeles there is a good spread of towns to visit: Santa Barbara with its mission and red-tile streets, Avalon on Catalina by ferry, Laguna Beach, Ojai's orange groves and San Diego at the outer limit. Traffic decides how far you get.

The trips out of Page are mostly to scattered heritage sites rather than towns. Choices include the pioneer buildings at Lees Ferry, the cliff dwellings at Betatakin and the small Western town of Kanab. The drives are long and the places small.

Los Angeles is one of the easiest big cities for keeping children entertained. It has Disneyland and Knott's Berry Farm, Universal's rides, the space shuttle, dinosaurs, tar-pit fossils and the Aquarium of the Pacific in Long Beach, and the mild weather helps.

Page suits families who are happy outdoors. A day on the lake or a short slot-canyon tour goes down well, and motel pools help in the heat. But nothing there is made for children, the summer sun is punishing, and the edges at Horseshoe Bend and the other viewpoints are largely unfenced above sheer drops.

Neither works well without a car, but Los Angeles at least offers some options. Metro lines link downtown with Hollywood, Pasadena, Long Beach and Santa Monica, ride-hailing is everywhere, and neighbourhoods such as Venice and Old Pasadena are good to walk around.

Page has no useful public transport. The lake, Horseshoe Bend and the parks all lie outside town, and the nearest big airports are hours away, so you need your own car for the whole stay.

Los Angeles is a real shopping city. Choose from luxury on Rodeo Drive, streetwear and vintage on Melrose, independent shops on Abbot Kinney, and flea markets at the Rose Bowl, plus surf and denim labels that reflect local style.

Page has souvenirs and supplies, with one exception worth your time. Navajo silver and turquoise jewellery, rugs and pottery are sold at trading posts and roadside stalls, often by the makers themselves.

Neither is cheap, but Page goes somewhat easier on the budget. Meals and fuel cost what they do in any small American town. The big costs are the paid canyon tours, the boats and rooms in busy months, and camping at Lone Rock or coming in winter cuts them.

Los Angeles adds expensive hotels, tax and tips on meals, a hire car and parking, and steep theme-park tickets. Taco trucks and free sights like the beaches and Griffith Observatory soften the bill only partly.

If you want an evening of music or theatre, only one of these two is a real option. In Los Angeles you can hear the Philharmonic at Disney Hall or, in summer, at the Hollywood Bowl, and see LA Opera at the Music Center. There are also rock rooms on the Sunset Strip, jazz in Leimert Park and some of the best comedy and improv anywhere.

Page has nothing comparable. At most you will find an occasional Navajo dance presentation or dinner show put on for visitors, or a local band in a bar. You cannot plan your evenings there around a performance.

Los Angeles has a real offer for a spa day, mainly in Koreatown's bathhouses, with hot and cold pools, scrubs and heated floors open late. Add the yoga studios and the luxury spas of Beverly Hills, though for true quiet people head out to Ojai or the springs of Palm Springs.

Page has only motel pools and a few hotel treatments. Its calm comes from desert evenings and dark skies, and the early starts there leave little time to slow down.