Speech anonymization techniques have recently been proposed for preserving speakers' privacy. They aim at concealing speak-ers' identities while preserving the spoken content. In this study, we compare three metrics proposed in the literature to assess the level of privacy achieved. We exhibit through simulation the differences and blindspots of some metrics. In addition, we conduct experiments on real data and state-of-the-art anonymiza-tion techniques to study how they behave in a practical scenario. We show that the application-independent log-likelihood-ratio cost function C min llr provides a more robust evaluation of privacy than the equal error rate (EER), and that detection-based metrics provide different information from linkability metrics. Interestingly , the results on real data indicate that current anonymiza-tion design choices do not induce a regime where the differences between those metrics become apparent.