I think I'm the first person in this thread who's actually seen both versions. I think they did a good job adapting the novel for international audiences. The original film was great and in a lot of ways couldn't have been improved upon much, but in several ways the American film was actually more faithful to the original novel (or at least the English translation; I have been told there are several ways in which the translation itself is pretty inaccurate, but do not speak Swedish and thus cannot investigate for myself); details such as
(SPOILER)Blomkvist's daughter being the one who figures out the "telephone numbers" are Bible verses and Blomkvist's sexual relationship with Berger were left out of the Swedish film but made it into the American film. On the whole I'd say the American film is about as good as a Hollywood adaptation could be; in a lot of ways it was pretty gratuitous to remake the film so quickly after the previous version but they did about as good a job as could be expected I think. I would actually say the American version was more visually impressive, though the opening credits are a blatant case of Design Student's Orgasm (see tv tropes if you're confused; I am not going to link to that time vacuum of a site) if ever I saw one. Also, it is worth noting Rooney Mara had gigantic shoes to fill playing a part previously played by Noomi Rapace, and did so admirably, basically stealing every scene she appears in.