Like in Euripides, Hippolyte does not desire Phaedra, but he is capable of desire, and like all of Racine's characters, even though love can feel like an uncontrollable force, humans are not merely manipulated by the gods -- they must bear the consequences of their actions as souls in this Christian understanding of the myth. Phaedra's language, although the play is set in ancient times, is explicitly Christian, as she speaks of her desire "To banish the enemy who made me an idolater," in her efforts to banish Hippolyte. ("Phaedra," translated by Tony Kline, line 294)
In terms of fatherly betrayal, while it is also true in Euripides that Hippolyte does not wish to dishonor his father, what is of greater concern to the young man is the honor he owes to the goddess Artemis, to whose chastity he has consecrated himself in a sacred fashion. This honor comes not from purity of thought, but in terms of making sacrifices to the gods and honoring their temples on earth. But Hippolyte loves and respects his father in Racine more than he talks of the divine: "Stop, dear Theramenes, show Theseus some respect," he shouts, even when most angry with his father. ("Phaedra," translated by Tony Kline, line 23) In contrast, Hippolytus in Euripides version, although the young man cares for his father, is much less internally tormented: He loves Artemis more than he loves any of the other characters in the play. "For thee, O mistress mine, I bring this woven wreath, culled from a virgin meadow, where nor shepherd dares to herd his flock nor ever scythe hath mown, but o'er the mead unshorn the bee doth wing its way in spring; and with the dew from rivers drawn purity that garden tends." (Euripides, "Hippolytus," MIT Classics Archive) Euripides' Phaedra in turn gives similar homage to Aphrodite.
But Phaedra in Racine works actively, internally to extinguish her love for Hippolyte rather than simply honoring or calling upon the gods. But rather than abandoning herself to passion, as she does in Euripides, Phaedra in Racine is much more controlled, initially, putting on a show of despising the boy so she may drive him away from her presence and remain faithful to her husband. "I die to evade this disastrous urge to confess," she states, again showing a strong sense of internal guilt, rather than a sense of being manipulated by fate and the gods. ("Phaedra," translated by Tony Kline, line 26) Rather than showing respect and worship for love, as personified in Aphrodite a la Euripides, Racine's Phaedra is openly tormented by sexual desires. Like Euripides' Phaedra, she is physically weakened and overcome by desire in the opening scenes, but Euripides Phaedra blames herself more than the gods, unlike her maid Oenone, stating that she must not confess her desire.
But perhaps the most notable difference between the two plays, is that in Phaedra, all of the characters have sexual desire. Hippolyte, rather than being chaste, loves another woman, Arcia, who threatens his chastity. "I flee, I confess, from young Aricia, / Last of a deadly race that conspires against me. ("Phaedra," translated by Tony Kline, line 50) Arcia, an Amazon, is also tormented by her love for Hippolyte. Thus, desire in Racine can affect all individual human beings, and individual human beings must be responsible for deciding to act as they do, even though desire can feel like an unstoppable force. In Euripides, the actions between the gods' favorites, at war because of a war between Aphrodite and Artemis, show humans to be pawns in a larger struggle. In Racine, rather than ending with a scene where the gods intervene in human affairs and settle all, the audience is left with the image of Phaedra stating, justly or unjustly in regards to her character: "It was I who cast my eyes, profane, incestuous, / On that son of yours, so chaste and virtuous." ("Phaedra," translated by Tony Kline, lines 1623-1624) Phaedra takes responsibility for all that has happened, and places the burden of her guilt on her soul alone.
Euripides. "Phaedra." MIT Classics Archive. Last updated 2005. http://classics.mit.edu/Euripides/hippolytus.html
Racine. "Phaedra." Translation by Tony Kline. 2003. http://www.tkline.freeuk.com/PhaedraActI.htm#_Toc88730163