Seeing this movie on the plane ride back from Paris made me curious to read the book. And it's very short, under 200 pages, so a very fast read. The film is so fresh in my mind that it's difficult not to compare the two.
I loved the film, and I liked the book very much. They did change some important things in the film, but since I saw the movie first, I guess I minded a lot less. (Then again, I read
A Little Princess many times before seeing the movie, and I didn't care at all how badly the movie butchered the book, because I loved that movie so much. So maybe it isn't inevitable for me to love whichever I encountered first.)
I read a criticism of the movie that it "simplified" the book, but I honestly don't see that. If anything, it deepened it. In the film, I liked that there was a confrontation at the end, that the death of one character wasn't glossed over, and that the movie treated all the sexual issues quite frankly and openly (as does the book, of course). There is definitely more drama in the film; in the book, we find out almost everything right from the start, whereas the movie holds it all back. I guess the novel is more subtle, and I can see where people might prefer that.
Of course, the character of Miss Jean Brodie is all Muriel Spark's creation, and an absolutely wonderful character she is, too. As amazing as Maggie Smith's performance is, the character of Jean Brodie is really created on the page, and I give Spark the bulk of the credit (though Smith should get some for a tour de force performance).
I think the novel (well, novella) is charming, and I recommend that you both read the book and see the film, and then let me know what you think. I'm especially curious about the experiences of people who read the book first. I think you'll enjoy them both, in whichever order you come to them.
"The Brodie set did not for a moment doubt that she would prevail. As soon expect Julius Caesar to apply for a job at a crank school as Miss Brodie. She would never resign. If the authorities wanted to get rid of her she would have to be assassinated." (Page 6)