When it comes to location-based services (LBS), user privacy protection can be in conflict with security of both users and trips. While LBS providers could adopt privacy preservation mechanisms to obfuscate customer data, the accuracy of vehicle location data and trajectories is crucial for detecting anomalies, especially when machine learning methods are adopted by LBS. This paper aims to tackle this dilemma by evaluating the tradeoff between location privacy and security in LBS. In particular, we investigate the impact of applying location data privacy-preservation techniques on the performance of two detectors, namely a Density-based spatial clustering of applications with noise (DBSCAN), and a Recurrent Neural Network (RNN). The experimental results suggest that, by applying privacy on location data, DBSCAN is more sensitive to Laplace noise than RNN, although they achieve similar detection accuracy on the trip data without privacy preservation. Further experiments reveal that DBSCAN is not scalable to large size datasets containing millions of trips, because of the large number of computations needed for clustering trips. On the other hand, DBSCAN only requires less than 10 percent of the data used by RNN to achieve similar performance when applied to vehicle data without obfuscation, demonstrating that clustering-based methods can be easily applied to small datasets. Based on the results, we recommend usage scenarios of the two types of trajectory anomaly detectors when applying privacy preservation, by taking into account customers' need for privacy, the size of the available vehicle trip data, and real-time constraints of the LBS application.