I ended up enjoying the back story and the character development in Fire more than I thought I would. I was not sure if I would like the Lisbeth Salander character better if she remained mysterious, but I thought Larsson kept her "more personal" character true to the character in the first book.
I thought the mystery part of the first book was more intriguing and more "mysterious". In fact, I'd call the first book an actual mystery novel and the second an action novel.
Although Fire starts with a disturbing scene, overall there was less really nasty violence in the second book. I remember finishing the first, thinking I would never want to see the movie, but I think I would see the second.
I liked the ending of Fire better. The only part of either of the books I really didn't like so far was the long, drawn out end to Dragon Tattoo. All the action was over, but there was one plot point that had to be wrapped up. Unfortunately it took like 75 pages to do it, and I spend the whole time just wanting the book to be over already. The end of Fire takes you right into the next book in the series.
If you are the second to last person on earth to read this series- and you like mystery/action/adventure novels and can handle some disturbing/violent scenes- I'd recommend reading them. I don't think they are THE BEST THING EVER, but they are good and entertaining books and I look forward to reading the last one sometime soon.