Specifying legal requirements for software systems to ensure their compliance with the applicable regulations is a major concern to requirements engineering (RE). Personal data which is collected by an organization is often shared with other organizations to perform certain processing activities. In such cases, the General Data Protection Regulation (GDPR) requires issuing a data processing agreement (DPA) which regulates the processing and further ensures that personal data remains protected. Violating GDPR can lead to huge fines reaching to billions of Euros. Software systems involving personal data processing must adhere to the legal obligations stipulated in GDPR and outlined in DPAs. Requirements engineers can elicit from DPAs legal requirements for regulating the data processing activities in software systems. Checking the completeness of a DPA according to the GDPR provisions is therefore an essential prerequisite to ensure that the elicited requirements are complete. Analyzing DPAs entirely manually is time consuming and requires adequate legal expertise. In this paper, we propose an automation strategy to address the completeness checking of DPAs against GDPR. Specifically, we pursue ten alternative solutions which are enabled by different technologies, namely traditional machine learning, deep learning, language modeling, and few-shot learning. The goal of our work is to empirically examine how these different 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.