I saw the Swedish version back in May of 2010, and had this to say:
Wednesday's decompression movies was, "The Girl with the Dragon Tattoo", two and a half hours of Swedish thriller/ whodunit while reading English subtitles. It is a VERY good movie for all of that, tightly written and well paced. The title character is fascinating, charismatic, and NASTY.
So now the movie has been remade in English, and I have seen it. The production version of this one are much higher, and I am told that this version is much closer to the book. The big difference between the two films, though, is the way the title character is presented. Rapace's Lisbeth was a TOUGH, a damaged but ultimately indestructible survivor; she acts tough and IS tougher. Mara's Lisbeth is much more vulnerable and tentative; she acts tough to cover her inner fragility. Mara's is closer to the book; Rapace's is both more believable, and more interesting.
I wouldn't mind seeing either or both versions again.