While she pays homage to De Palma in several shots, Peirce is also clear about where they differ. The first is the feminism (or style of feminism—I'm not yet convinced that De Palma was a misogynist). Peirce is obviously conscious of the body of criticism that exists around the first film, and she deliberately rolls up her sleeves and turns some things around. For example, some scholars disliked the fact that Chris and the girls were so mean to Carrie—they saw this as reinforcing stereotypes of women as "catty."
This strikes me as a weak claim, like a Christian complaining that Margaret White exists simply to poison everyone's opinions of all Christians. Unfortunately, there just are some mean young ladies in high school—and some nasty old ladies with unbiblical views of sex in the church.
But Peirce switches it up. Chris is no longer the mastermind of the pig's blood prank. Rather, she's a victim of patriarchy—it's her boyfriend Billy's idea, and he pressures her into it. He even inducts her into the boy's club by offering Chris the knife (saying "here man," no less) to take her own stab at the pig. She takes the knife from him and strikes, to the glee of the boys—this makes the scene, otherwise a homage to Lord of the Flies, a nod to the feminist idea of unconsciously seeking the "male gaze," of women getting a kind of Stockholm Syndrome when it comes to patriarchy. The inclusion of Chris's alpha male father in the film—present in the book but not the De Palma adaptation—reinforces this. And Peirce also got rid of De Palma's main "phallic symbols," replacing them if not subtly then at least reservedly with feminine anatomical symbols.
And finally, Carrie's character: Moretz portrays her surprisingly well, given that Spacek was much odder-looking. But Moretz adds the dynamic of extreme youth: she is convincingly undeveloped compared to the girls around her, whereas Spacek looked young but not childlike.
The most important change in the main character, though, is that she grows to control her telekinesis and use it much more consciously. In De Palma's film her telekinesis was linked more directly to hormones, unconsciously lashing out. This Carrie has control over it—but her love of the power, visible in Moretz's transformation from innocent youth to sinuous Succubus, are a new element in her downfall.
But as interesting as the various takes on the gender issues in the Carrie story are, the most surprising contrast between De Palma and Peirce is their approach to Christianity.
As Joseph Aisenberg points out in his landmark book on Carrie, Brian De Palma's adaptation is all Law. He let Piper Laurie (who played Carrie's mother) think the film was straight satire for much of the original shoot, and it shows. He has no explicit patience for religion—but his sense of justice speaks volumes. The director once said of the plot that "obviously, Carrie should be able to go to the prom. And obviously, when all those people do all those terrible things to her, they should 'get it.' And they do get it. And obviously her mother, who is trying to kill her, should get it, and she does. And obviously, when [Carrie] committed matricide, she should die, and she in fact dies."