How do bird identification apps for cellphones compare with the popular identification books?
If there is a related book, chances are there is a good app to go with it. No book, then the quality varies.
Apps can be great. The good ones offer multiple photos, recordings of songs, video, checklists and website links in addition to text and maps. Recordings of songs, for example, can make a big difference. The songs and calls on the apps I own are what I appreciate most.
On the Apple app store website I found 42 apps that I consider more or less pertinent to the task. Some are better than others. Some are way better. Some aren't (limited content). Many are for foreign birding locations.
As you shop, look for names you know: Audubon, Sibley, National Geographic, Cornell Lab of Ornithology, for example. If you liked the book, you'll probably love the movie.
Like most things, app quality comes with a price. The best apps contain the information found in the best books plus more.
You can buy apps that contain all North American bird species, as do the basic ID books. You also can find apps containing the birds of almost any country with a birding reputation.
Before you buy, read the fine print. Read the reviews. Check operating system compatibility; some aren't available for Android devices, for instance.