Exaggerated: Budou's past, lovingly detailed and revealed throughout the series, is a Trauma Conga Line of abuse, angst, suffering, and misery that would take years upon years of therapy to unravel.
Justified:
Queen Sangria has taken blood collected from one of Ichigo's battles with her and used her dark magic to construct a copy of Ichigo from it, who she names Budou. Although they share similar powers, the taint of evil has twisted her into something far more sinister. After being defeated by her twin, the dark magic's hold over her is exorcised, leaving her a more complete copy willing to join Ichigo's side.
All of the Magical Girls are from a Always Lawful Good Race. Budou was trained to be evil, but still instinctively knows what she is not supposed to do what she is doing. When Ichigo defeats her, she offers her an opportunity to defect. She does.
Parodied: Budou is an obviously blood-crazed psychopath, but after being beaten by Ichigo, she is tied up in a scene reminescent of A Clockwork Orange and brainwashed with friendship speeches until she breaks and starts espousing the power of friendship on her own.
Deconstructed: Budou's emotional scars run so deep that they can't be healed just by losing a fight with her rival and listening to Ichigo's claims of acceptance. Ichigo can claim to understand all she wants, it doesn't matter to Budou. She continues to antagonize Ichigo until she either overpowers and defeats her or Ichigo is forced to take her down, sending the young heroine into a Heroic BSOD afterwards.
There is no direct counterpart to the heroic magical girl; Queen Sangria just uses a Monster of the Week tactic.
Ichigo's counterpart among the villains is Tamanegi, a sadistic Dark Action Girl who's older and more experienced, and sees Ichigo as an irritating little goody-two-shoes.
Enforced: "The boys in merchandising want another cute girl to put on the merch. How about giving our heroine a dark counterpart, so we can just use a slightly different palette?"
Lampshaded:
"Why couldn't I be a happy girl like you, Ichigo? Why does my fate have to be so harsh?!"
Alternatively, "Oh, come on! She wears black, has a Dark and Troubled Past, and is abused by her master! All you have to do is beat her up and rant about friendship, and she'd Heel Face Turn in a heartbeat!"
Invoked: Queen Sangria intentionally sought out mentally scarred young girls that she could indoctrinate into her ranks and set against any would-be heroes.
Defied: After the first fight between Ichigo and Budou, Queen Sangria sees hesitation in Budou's eyes upon her return, and, refusing to take the chance that her servant could be turned against her, she obliterates her.
Discussed: "Sangria is just using you, Budou! You mean nothing to her! I'm going to befriend you so we can get ice cream together! Finishing Move: Sun's Fury!"
Played For Drama: The constant battles push each girl, Budou and Ichigo, into an emotional crisis. When they next confront each other, they decide to join forces - to defeat Ichigo's mentor as well as Budou's master.
Let's go back to Dark Magical Girl. Don't worry! As long as we're together, there's nothing we can't do!