This is one of the better versions of these stories in my opinion, and is particularly suitable for older children who are ready to move beyond simple children's stories. The stories are a bit "straighten up" for contemporay audiences, but they retain the language and the fanatastic elements that people turn to these Tales to enjoy. The stories also retain some of the violent and cruel plots twists of the original, another reason you may not want to use these as bedtime stories for little children.
All the major stories and most of the minor ones are included, and the "frame story" of the Shah and his clever wife is carried throughout the book very nicely. Each story told by Shahrezade serves a secondary purpose of advancing the tale of the royal couple's evolving relationship, and so the ending is more truly satisfying than in almost any other version of the Arabian Nights.
The illustrations are good as well, and add to the storyland feeling of the tales. (The only quibble I have hear is with the white European look of most of the characters in the drawings.)