I would say that one of the primary differences between both the novel and the film is one of visualization. Daldry's film presents a projection of what Cunningham's novel might appear to be. For those who really immerse themselves in the dynamics of the novel, this might be a bit jarring. What is envisioned in the mind when reading a work like The Hours is always different when projected on the screen. The beauty of literature exists in how it lingers in the mind's eye, pristine and apart from any other interpretation. When placed on screen, this vision is tainted, to an extent. This becomes one of the differences.
I think that another difference is that steady and constant interplay of the novel where one has to forge the connections between the different narratives is presented in a different way in the film. In reading the book, the reader must make these connections themselves, while in the book, these connections are made by Daldry and the film's writer, David Hare. In this, there is a bit of a transferal difference than what would be in the book.
The characterization of Clarissa is less internal in the film than it is in the text. Clarissa's own challenges between understanding her own identity and the internal ruminations that accompany it are not as present on screen, where they are more implied. Along these lines, the feelings of insecurity and doubt about Clarissa's motherhood are not as strongly evident in the film. Julia occupies more of a role in the text than in the film, where she is prominent in about two or three scenes, with one of them being more symbolic in her interactions with Laura. Certainly, the redemption that is hinted at in the end of the text with Clarissa's embrace of the attachments around her are not as strongly reflected in the conclusion of the film with the suicide of Woolf bookending the film. One recognizes the action, but the film's ending is not one where the hint at redemption in the book is experienced, as much. I think that a final difference would have to be the presence of the Glass score in the film that really does impact how one views the film and thus, the text. The driving force that the musical score of the film provides captures a certain type of emotional energy that helps to bring out the characters in a manner that escapes language. Reading the work with the score in one's mind or even in actuality can bring about a different literary experience. This is yet another way in which the film and book differ.