Machine learning based classifiers that take a privacy policy as the input and predict relevant concepts are useful in different applications such as (semi-)automated compliance analysis against requirements of the EU GDPR. In all past studies, such classifiers produce a concept label per segment (e.g., sentence or paragraph) and their performances were evaluated by using a dataset of labeled segments without considering the privacy policy they belong to. However, such an approach could overestimate the performance in real-world settings, where all segments in a new privacy policy are supposed to be unseen. Additionally, we also observed other research gaps, including the lack of a more complete GDPR taxonomy and the less consideration of hierarchical information in privacy policies. To fill such research gaps, we developed a more complete GDPR taxonomy, created the first corpus of labeled privacy policies with hierarchical information, and conducted the most comprehensive performance evaluation of GDPR concept classifiers for privacy policies. Our work leads to multiple novel findings, including the confirmed inappropriateness of splitting training and test sets at the segment level, the benefits of considering hierarchical information, and the limitations of the "one size fits all" approach, and the significance of testing cross-corpus generalizability.