Software systems involving personal data processing must adhere to the legal obligations stipulated both at a general level in the General Data Protection Regulation (GDPR) as well as the obligations outlined in data processing agreements (DPAs) that highlight specific business needs. DPAs are regulated documents laying out data processing requirements to ensure that personal data remains protected. In other words, a DPA is yet another source from which requirements engineers can elicit legal requirements. Eliciting requirements that would cover the complete set of obligations requires that the DPA is complete according to GDPR. In this paper, we propose multiple automated solutions for checking the completeness of DPAs against GDPR provisions. Specifically, we pursue ten alternative solutions enabled by different technologies, namely traditional machine learning, deep learning, language modeling, and few-shot learning. The goal of our work is to empirically assess how these technologies fare in the legal domain. We computed F2 score on a set of 30 real DPAs. Our evaluation shows that best-performing solutions yield F2 score of 86.7% and 89.7% are based on pre-trained BERT and RoBERTa language models. Our analysis further shows that other alternative solutions based on deep learning (e.g., BiLSTM) and few-shot learning (e.g., SetFit) can achieve comparable accuracy, yet are more efficient to develop.