I wasn't all that impressed with the first book. That was, until I saw the movie, and then all of a sudden my opinion of it greatly improved. So much so that I was intrigued enough to read the second book. I'm happy I did, because it was so much better than the first!
One thing I found annoying in the first book was the first 100 pages or so were totally useless and completely filled with tiny detail after tiny detail. The kind of details that you think must be important to the story later on - because why else would the author include them? - but they weren't. I found this to be true in this book's introduction as well, but the difference was the story was more interesting.
Another thing about the first book that I didn't particularly like was how dark and disturbing it was in parts. If you have read the book, you know what I'm talking about, if you haven't read the book, let's just say there are a few scenes that are squirm-worthy. This wasn't the case in this book. The main female character, Lisbeth Salander, was portrayed more like a heroine than a victim. It was a refreshing view point of the character, and I liked that Larsson showed both sides of her in the two books.
The book was fast-paced and really interesting. It was full of surprises and, even though the book was over 700 pages, it flew by (thanks, in part, to reading most of it on my new Kindle).
Overall, the book had some of the downfalls of the first (too many names and places to keep track of, a 100-page introduction and tiny details that didn't matter to the story), but the writing was much better and the story was more interesting. Since I gave the first book a 3.5/5, I'm going to give this one a 4/5 and hope the last book of the series can top it.