You don't say if either of you got the job. Is that even known yet? If you got hired and she didn't, there doesn't seem to be much to complain about. If it's the other way around, see below.
It is often assumed that the resume/CV (assuming it's true, and references are often used to do that) shows whether a job seeker has the skills needed. Interviews are often about determining if a candidate will "fit" in the organization as much or more than if they have the technical skills needed to do the job. To do this, it's frequently considered desirable to put the candidate into a more relaxed frame of mind than they probably are when they walk into the interview. As such, by having you discuss the answer you had prepared for their case study, they may have hoped to put you into familiar territory and thus relax you. That raises the question of what was your answer in comparison to the other candidate's answer. Was yours more technical than hers? If so, that probably explains why you were asked more technical questions.
Keep in mind that no two interviews are ever going to be identical. Some organization may make a point of having questions prepared in advance to avoid (potential) appearances of being unfair, but no two candidates will answer the same and different answers will lead to different follow up conversations.