One of the main features in mobility sharing applications is the exposure of personal data provided to the system. Transportation and location data can reveal personal habits, preferences, and behaviors, and riders could be keen not to share the exact location of their origin and/or destination. But what is the price of privacy in terms of decreased efficiency of the mobility sharing system? In this paper, for the first time, we address the privacy issues under this point of view and show how location privacy-preserving techniques could affect the performance of mobility sharing applications, in terms of both System Efficiency and Quality of Service. To this extent, we first apply different data-masking techniques to anonymize geographical information and then compare the performance of shareability networks-based trip matching algorithms for ride-sharing, applied to the real data and to the privacy-preserving data. The goal of the paper is to evaluate the performance of mobility sharing privacy-preserving systems and to shed light on the trade-off between data privacy and its costs. The results show that the total traveled distance increase due to the introduction of data privacy could be bounded if users are willing to spend (or "pay") for more time in order to share a trip, meaning that data location privacy impacts both efficiency and quality of service.