Really not one book, but two. The first part of little women was written first and published and due to its success Alcott wrote the second part which is a sequel and not a true second part.
The first part is well written, but its aim is mostly a moral one, so while there is a continuous charm, there is a kind of unreality to it that can often be found in literature designed to morally improve children. For instance, the character of the mother is so morally perfect as to have no personality at all, and while no one dies, the threat of death is there and its reality is moderated. It is charming, well written and there is something modern and contemporary about its prose.
Something has changed in the second part, and as the girls have grown Alcott allows a deeper exploration of the themes and the characterization is deeper and the human interaction more real. There is more of an infusion of Dickens into her style and the book benefits from it. There is also a clear benefit on focusing more on Jo who is the only truly fascinating character in the novel. The second part does give into ersatz sentimentality from time to time, but it is the second part that makes the book deserve to be a classic.
A flawed but mostly charming book.
Update: I stand by what I wrote above, but at the time I had not read a great deal of children's literature aimed at girls. As I read more of it and get to understand this sub-genre better, my appreciation for this book goes up. Bumped to four stars.