Although Viola in She's the Man may be discriminated against, because of her gender, Shakespeare's Viola has never been allowed to be assertive in a physical manner because the way women are socialized. This is why Shakespeare's Viola is both a sadder and more vulnerable character throughout Twelfth Night, in contrast to the more tomboyish Viola in the modern film who can fend for herself.
The romantic aspects of the original are relatively the same: Viola loves Duke Orsino (simply known as "Duke" in the film), Duke loves Olivia, and Olivia loves Viola, whom she thinks is a boy. But there is none of the melancholy that characterizes Shakespeare's comedy in this frustration of desire. Olivia rejects men because she is pining for her brother, who is dead, and when she allows herself to fall in love again, she finds herself cruelly rejected despite the fact that "he" seems to be her social inferior, Orsino's servant. Sebastian comes to love Olivia, but must reject his friend Antonio. More is at stake in the film, namely the character's entire romantic lives. The film, which is about teenagers and their relationships, never suggests the characters will get married or that their various couplings and uncouplings are to be taken very seriously beyond the world of high school. When Viola talks about a sister who died for a man's love, she is seriously speaking of herself and her own passionate feelings for Orsino -- instead, Viola and Duke in the film have a more funny "man to man" bonding about what women really want.
The very sinister "madness plot" and the characters of Toby and Andrew in Twelfth Night are toned down in She's the Man. In Twelfth Night, Olivia's maid Maria, Sir Andrew Aguecheek and Sir Toby Belch convince Olivia's puritanical overseer Malvolio that Olivia is in love with him, and cause him to adopt strange mannerisms, like wearing yellow stockings and grinning constantly. Although this plot may seem like a "side show," it shows how desire between social inferiors and superiors is never really allowed to transgress class boundaries in Shakespeare. In the case of Viola/Cesario and Duke Orsino's eventual love affair, Viola is really noble, but Malvolio is not. (Viola calls herself a "gentleman" at one point to Olivia). The unsuitability of Malvolio for Olivia suggests that while it is alright to love someone who seems "wrong" -- such as Olivia's love for the apparently poor (but really noble) Sebastian, to "really" violate the rules of class division throws one squarely into the arms of a horrible social upstart Malvolio. In She's the Man, there is no parallel class commentary, and the tricksters are more class clowns than really malevolent.
In terms of the tone of the comedy, other than the "madness" plot, there is relatively little broad farce in Twelfth Night. This is one rather surprising comparison between the film and the play: although Shakespeare's Viola is less socialized to male roughhousing, there is relatively little humor based on the differences between female and male anatomy in the play. In She's the Man, many scenes revolve around Viola trying to finesse having to be a "shirt" when the boys play "shirts and skins," for example, and dealing with her new boarding school's "shower situation." Some of these comedy elements are very predictable, and could occur in any cross-dressing film, even not one based upon Shakespeare, even in a film not based upon a woman being dressed as a man. In Shakespeare, the gender-bending humor derives more from the character's inability to say what they really feel -- Viola cannot explain to Olivia why she does not love her, for example. But this is not entirely to do with gender, as every character believes that they are in love with someone who is in love with someone else. Thus Shakespeare's comedy is more fundamentally based upon emotion, character, and even social class than physical difference unlike She's the Man.
Shakespeare, William. Twelfth Night. The Shakespeare Homepage. April 22, 2009.