Recent advancements in textless speech-to-speech translation systems have been driven by the adoption of self-supervised learning techniques. Although most state-of-the-art systems adopt a similar architecture to transform source language speech into sequences of discrete representations in the target language, the criteria for selecting these target speech units remains an open question. This work explores the selection process through a study of downstream tasks such as automatic speech recognition, speech synthesis, speaker recognition, and emotion recognition. Interestingly, our findings reveal a discrepancy in the optimization of discrete speech units: units that perform well in resynthesis performance do not necessarily correlate with those that enhance translation efficacy. This discrepancy underscores the nuanced complexity of target feature selection and its impact on the overall performance of speech-to-speech translation systems.