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Electroencephalogram plays an essential role in analysing and recognizing brain-related diseases. EEG has been increasingly used as a new type of biometrics in person identification and verification systems. These EEG-based systems are important components in applications for both police and civilian works, and both areas process a huge amount of EEG data. Storing and transmitting these huge amounts of data are significant challenges for data compression techniques. Lossy compression is used for EEG data as it provides a higher compression ratio than lossless compression techniques. However, lossy compression can negatively influence the performance of EEG-based person identification and verification systems via the loss of information in the reconstructed data. To address this, we propose introducing performance measures as additional features in evaluating lossy compression techniques for EEG data. Our research explores if a common value of CR exists for different systems using datasets with lossy compression that could provide almost the same system performance with those using datasets without lossy compression. We performed experiments on EEG-based person identification and verification systems using two large EEG datasets, CHB MIT Scalp and Alcoholism, to investigate the relationship between standard lossy compression measures and our proposed system performance measures with the two lossy compression techniques, discrete wavelet transform—adaptive arithmetic coding and discrete wavelet transform—set partitioning in hierarchical trees. Our experimental results showed a common value of CR exists for different systems, specifically, 70 for person identification systems and 50 for person verification systems.