Okay, so the most obvious shadow/foil for Buffy is, of course, Faith. We’ve got the palette swap (hair-wise), similar roles, and the whole but-for-the-grace-of-XYZ situation. After Faith’s turn to the Dark Side, Buffy realizes how easily she could have been Faith had she not been grounded by her family, friends, and Watcher. (Other foils for Buffy exist, as well, like Kendra, Cordelia, and even Glory). Yet I think there’s an interesting parallel set up between Drusilla and Buffy.
This connection is most obviously evidenced in BtVS 2x13 “Surprise”, where scenes involving Dru’s party and Buffy’s party are directly paralleled. Similarly, in BtVS 2x14 “Innocence”, the second half of that two-parter, Angel’s separation from Buffy allows his return to Drusilla. She gleefully proclaims that they are “a family again”, the same words she will later use in BtVS 5x14 “Crush” when trying to persuade Spike to return with her to Los Angeles.
However, a more interesting connection has to do with Drusilla’s insanity. Before becoming a vampire, she had the Sight (AtS 2x7 “Darla”). Deeply religious as a human, she was driven to madness by Angel, who then sired her. Buffy, meanwhile, has had her own brushes with mental unwellness, or at least the perception of such. As revealed in BtVS 6x17 “Normal Again”, she was briefly sent to a psychiatric hospital shortly after she was Called. Like Dru’s visions, her “delusions” were based in reality, albeit a reality outside of the grasp of normal humans.
When disappointed or angered, Drusilla often breaks down completely as in “Surprise” when the flowers for her party are “not right”. Buffy is, of course, more stable, but she goes into a similar state in BtVS 5x20 “Spiral” after Dawn is taken by Glory. It is very difficult to reach either Drusilla or Buffy when they go into this emotionally comatose state; Spike and Willow, respectively, manage it in the aforementioned episodes, but Willow can only achieve this through magical intervention.
Drusilla and Buffy also share Spike as a love interest, and although it is difficult to compare their relationships, some similarities still arise. Both Drusilla and Buffy loved Angel first, a sure source of insecurity for Spike. While Drusilla adores Spike’s monstrous qualities, his humanity eventually proves too noxious to her (BtVS 3x8 “Lovers Walk”); meanwhile, before Spike regains his soul, Buffy regards him as too much of a monster for her to ever love (BtVS 6x13 “Dead Things”). In both cases, a comparison results with Angel(us) - Spike is too “human” (as the Judge says in “Surprise”) for Drusilla but still obviously vampiric (unlike ensouled!Angel).
In temperament, too, there are interesting contrasts between Drusilla and Buffy. Whereas Buffy worries in BtVS 5x18 “Intervention” that “being the Slayer is turning [her] to stone” and making her into a machine, Drusilla depends entirely upon emotion to make her decisions. As she tells Spike in “Crush”, she doesn’t “believe in science…all those bits and pieces no one’s ever seen” and “[relies] on eyes and heart alone”.