Okay, finally got a chance to sit down this weekend and watch the Swedish film. And my verdict is that I prefer the American version.
The acting in both is top notch. I actually think I like Chloë Moretz more than Lina Leanderson, and Kåre Hedebrant more than Kodi Smit-McPhee; however, all four provide excellent performances.
American production values seem higher, the film is more crisp, etc. But that's generally par for the course, and I feel a little bad about holding that against the Swedish film. I guess my only legitimate technical complaint is that in the Swedish film there is more of a sense of the set. Things look more staged and the environments, with several exceptions, feel a little artificial.
The real deciding factor for me is the story. The Swedish film tries to introduce more characters from the novel, without really staying more true to the novel's narrative, or doing enough work to justify those characters. Specifically, I feel that the characters of Lacke, Virginia, and Gösta were extremely underdeveloped, especially for the role they played. As I read the novel I find them to be much more believable and sympathetic characters, but the film just presents them in a disjointed fashion and leaves me very confused about their identities and motivations. I find this particularly crippling with Lacke and Virginia who do have such interesting roles in the story, yet we learn almost nothing about in the film. The American film circumvents this by relegating them to minor characters and giving Lacke's role to the police detective (who needs no motivation other than his job to look into the murders, a weak motivation? Yes. But it beats completely glossing over the rationale behind Lacke's actions, relationship to Virginia, and response to Jocke's murder in the Swedish film).
Also I think Håkan is underdeveloped in both films (which I suppose is a necessary evil since so much of his identity and history are given in flashback in the novel). However, while the Swedish film leaves him motivationless (apparently not wanting to bring in and explain his pedophilia) the American film changes his motivation and allows us to infer a succinct (and really skillfully introduced) explanation for his actions. While I am generally for staying true to source material, I still enjoy the presence of that explanation other than the complete absence of one in the Swedish film.
I also do not appreciate the Swedish film's blink and you'll miss it introduction of Eli's, shall we say for the sake of not spoiling anything, physical abnormalities. I would rather omit it entirely than have something like that sprung on me with no explanation or role in the story. Once again it is taking the book to give me an appreciation of the meaning behind that story element.
In summation: When watching the Swedish film I feel like an observer being given somewhat disjointed views. It leads to a feeling of authenticity. There is something voyeuristic about it. But at the same time it often leads to confusion and a lack of sympathy with the characters. Further it gives the impression that the director wants you to have already read the book before seeing it, as he is astonishingly lax in developing multiple character and plot elements. The American one feels more like being told a story (which loses some of the visceral impact) and fewer questions are left when the narrative is done (other than Eli/Abby's past which neither film explores).
The end result is debatable but I know I caught myself checking the time more during the Swedish film. Both have a similar run-time and I know some critics are complaining about that. I think the American film earns and fills its 2 hours. I am not sure that the Swedish film does so (paradoxically it seems to both earn less and need more <_<). And I found that I walked away less disturbed from the Swedish film than I did from the American, which I think should really kind of be the rule of thumb about this sort of thing.
Although for sheer disturbance power the book is a must. I am 2/3 through and find it incredibly interesting and engaging.
They are both fine movies and are definitely going into my collection, I just think that the American one is a slight bit better in its handling of the story (especially if you are not going to read the book beforehand).