Privacy preserving record linkage (PPRL) addresses the problem of linking records that represent the same individuals across several datasets without revealing sensitive information of the individuals. To this end, the records to be linked are processed first, then exact or approximate matching techniques are applied to the encoded records to identify the matching record pairs. Obviously the encoding employed in the data processing step plays a key role in achieving a good linkage performance on the linkage quality and privacy. However, it is known that in PPRL a theoretical framework is missing that allows a comparative evaluation of different encoding techniques. Linkage quality is typically evaluated experimentally, and for the privacy, there are even no commonly accepted privacy measures available that allow an objective evaluation. This paper attempts to provide a comparative study of two popular binary encoding schemes: the one-hot encoding and Bloom filter encoding, in the context of PPRL. Theoretically, we show that both encodings are similarity-preserving (and thus the linkage quality is not degraded). Moreover, for privacy, we borrow the concept of unicity distance from cryptography, and consider security measures that take into account the number of the intercepted ciphertexts at the attacker, while considering either a ciphertext-only or a known plaintext attack model. Applying these measures and the bounds established, we show that the Bloom filter encoding with appropriate parameter choices could outperform one-hot encoding in the privacy aspect. Last but not least, we show that the unicity distance alike concepts also bring insights into both assessing the effectiveness of the hardening techniques and selecting the optimal parameters of the Bloom filter encoding. Therefore, they could be used in the comparative evaluation for different encoding techniques or the same encoding technique with different parameter choices.