Despite some improvements in compliance metrics after the implementation of the European General Data Protection Regulation (GDPR), privacy policies have become longer and more ambiguous. They often fail to fully meet GDPR requirements, thus leaving users without a reliable way to understand how their data is processed. We present a novel corpus composed by 30 privacy policies of online platforms and a new set of annotation guidelines, to assess the level of comprehensiveness of information. We focus on the processed categories of data, classifying each clause either as fully informative or as insufficiently informative. In our experimental evaluation, we perform 6 different classification and detection tasks, comparing BERT models and generative Large Language Models.