I watched this at the theaters today. It's surprisingly faithful to the Swedish version in a large number of ways. It has some changes and a few reworkings.
Is it better or worse? I'm not sure. Is it worth watching? Without a doubt.
The casting choices are excellent. The boy (renamed from Oskar to Owen) is played by a somewhat taller but still waif-thin actor, and his voice is still childlike and vulnerable. The girl (renamed from Eli to Abby) is played by a fair-haired actress, but with a wonderfully androgynous face. The first real scene with them at the jungle gym in the snowy courtyard features her in a backlit profile, partially obscured by a hood. Her nose and mouth in that light make her look like a young boy - further hinting at the backstory.

There is even less of the pedophile undertone in this version. The older man does not ask to sleep with her. They share one moment in the kitchen when she lays her hand on his cheek and he holds it there for a second or two with his own - an oddly understated and subtle moment that I had not expected from an American director. Eli's backstory from the book is even more obscure in this version. Abby faithfully divulges "I'm not a girl" once or twice, but the subplot with her pedophile "caretaker" is entirely obscured, and the moment where Owen watches her change is completely mundane in this version (whereas it was one of the single most disturbing scenes in the original). Some might hold this to be a sign that an American film can err on the side of subtlety and suggestion - but the honest truth probably lies more in the desire to avoid controversial themes. Certainly in almost all other respects, the remake movie tends towards greater disclosure, not less.
The parents lose the most screentime in this adaptation. In the Swedish film, there is a wry endearing scene where Oskar and his mother brush their teeth together, grinning at each other. It's a brief scene but it reminds the viewer that there is at least some normalcy in the boy's life. Likewise, Oskar visits his estranged father in a warm scene in a cabin, but with hints of internal conflicts with alcohol and a special male friend. In the American film, the father is reduced to a disembodied voice over the telephone, and his mother is a faceless and almost-silent monument to despair. We see more of her curled up asleep with the blaring TV than we do of her awake. The net effect of all this is for a much more desperate view of Owen's existence than Oskar's. Outside of his candies, Owen has nothing else to keep him grounded... all the more reason to see Abby as a friend, a source of comfort, an escape.
The American version has a firm date - it's set in 1983, and it brings up more pop cultural references from that era. Kids play Mrs. Pac Man at the arcades, and one of the employees there dresses like Boy George. Owen puts on contemporary music on vinyl and cassette tape. Reagan reassures Americans that God is on their side. TV channels ask if parents know where their children are, at 10 p.m. The cultural nods are not intrusive, but they are much more obvious than in the Swedish version, and they will probably hurt the film's international reception in a way that the Swedish version escaped.
A few key scenes have been rewritten entirely: the pedophile's capture is done in a much more dramatic fashion than the original... with a few heartstopping moments when it seems like he might just get away with it. The first female victim is introduced in a completely different context. There is also a new character in the form of a police investigator, who assumes some of the plot roles of minor characters in the original. But the general plot of the movie is very similar, with several scenes immediately recognizable to anybody who had seen the first movie.
Perhaps the biggest difference in this movie is the treatment of the most violent scenes. Where "Let The Right One In" seemed to have a more moderate approach, "Let Me In" tends to look the monstrous aspects full in the face. This is a mistake, in my opinion. The Swedish production featured heavy use of digital special effects, and the American production seems more of a latex-and-rubber production, in keeping with Hammer Film Productions' checkered history. The effects fell a little flat for me: in each case, I felt like I was looking at an actor in a mask rather than the horror in the flesh. This is a step back from the Swedish original, where all the horrific "face-to-face" scenes felt much more organic and real. Abby in the American version has two faces - the girl and the monster. It's a strangely unsatisfying simplification from the Swedish version, where Eli had a very brief eloquent moment as a sorrowful crone, beseeching Oskar to see the world as she does, through bloodstained eyes.
In its defense, the first time you see the American film's Abby on the hunt will almost assuredly make you jump... as will every subsequent time too. The American movie wins on choreography, while the Swedish version wins on cosmetics.
The infamous swimming pool confrontation at the end is very similar to the Swedish version, but with an obvious shift in focus. Where the Swedish ending showed the violence and death obliquely - as distant silhouettes falling into the water - the American ending keeps us eye-to-eye (so to speak) with all the action. For me, it was a clear lesson in the limitations of explicitness, and the superior power of suggestion. The musical score also feels like it follows this philosophy, too. It's been some time since I've seen the Swedish, so I can't immediately recall the style of the musical accompaniment, but the US version is fairly heavyhanded with the use of mood music.
This is still a very classy movie, as much about the alienation and cruelty of childhood as it is about vampires. There are some beautiful new touches absent from the Swedish original, as well: Abby's handwritten notes are all written in the antique flowing script of a lady many centuries older; and when Owen discovers photographs of her with a boy in glasses, the astute viewer will immediately understand the root of his sudden terror.
Worth watching if you liked the original. Doubly so if you've never seen it.