For the most part, it is a direct adaptation of the film. However, there are some noticeable differences, especially in the 1987 original...
The story begins with the introduction of David Q. Dawson, instead of Olivia Flaversham and her father, and mentions that he had returned from military service in India, rather than Afghanistan like in the movie. (The Mouse Works reprint replaces "India" with "Afghanistan.")
Dawson mentions he was supposed to go to Basil of Baker Street's flat to rent a room. In the film, he does not mention anything like this, and has never heard of Basil until he reads the newspaper clipping from Olivia.
Although the illustration shows Basil having just unmasked from his Chinese mouse disguise as seen in the film, the text on the page describes Basil having disguised as an old beggar, wearing a ragged coat, a crumpled hat, and a false beard and nose. (This was corrected in the Mouse Works reprint, referring to his disguise as "a figure in a long, red robe." Interestingly, concept art remains showing Basil in that disguise, suggesting the book was basing itself on early concepts rather than making an outright mistake.)
Although Basil fires his gun at the pillows, he does not attempt to find the bullet, and does not get depressed and start playing his violin.
The mouse Ratigan has Felicia eat is not Bartholomew as in the film, but a different-looking drunk mouse. Additionally, the scene where he threatens Hiram Flaversham comes afterward, rather than before like in the film.
When Olivia sees Fidget the Bat peering into Basil's window, it's menioned that he simply turns and walks away afterward; in the film, he falls from the window.
Toby is shown with the ability to talk. In the film, he does not talk, but instead barks, howls, and growls like a real dog.
In the toy shop, Fidget does not turn on various musical toys to create a diversion, or hide in a baby's bassinet to catch Olivia as he does in the film.
Miss Kitty does not appear in the bar scene, nor to the drugged beers. It is mentioned that the sailors in the bar are singing a song, and Dawson, being "a little tipsy," wants to join in, but accidentally causes a big fight.
Fidget does not get into the bottle and pose as Olivia to trick Basil and Dawson as he does in the film. Instead, he is with Ratigan and the other henchmen, watching as Basil and Dawson attempt to free the real Olivia.
It is not mentioned that Basil goes into a depression among being captured by Ratigan, and the elaborate trap does not feature a camera set to take Basil and Dawson's photo after being killed. Ratigan also mentions the song on the record being "The Executioner's Tango", but in the film, the song is actually called "Goodbye, So Soon".
Basil saves Queen Mousetoria from Fidget and Felicia before the diamond jubilee begins, unlike in the film, where the ceremony was already in progress. Additionally, Basil does not take control of the robot Queen as he does in the film; instead, he simply calls Ratigan an "impostor" and destroys the robot with one swift kick.
When Basil and his friends chase Ratigan's Blimp, Dawson is back in his normal clothes, unlike in the film where he still had part of his sailor disguise on. Additionally, the "gondola" to Basil's aircraft is made of wooden planks in the book, while in the film it is made out of a matchbox.
Fidget is not thrown from the blimp as he is in the film. He is last seen right before the blimp crashes into Big Ben (which is simply mentioned as "the clock tower" throughout the book), and mysteriously disappears after that, having possibly died in the crash.
Basil saves Olivia from being crushed by the gears by swinging on a rope, instead of riding a chain like in the film. Additionally, Ratigan does not lose it and become wild and feral as he does in the film, and still looks like his normal self when fighting Basil. The text mentions Ratigan being catapulted off the clock when it strikes the hour, while Basil holds on tight and jumps into his aircraft with his friends, while the illustration shows Basil riding the propellor part of the destroyed blimp, as he does in the film.