This paper investigates the utilization of Low Earth Orbit (LEO) satellites for vehicle localization and conducts a comparative analysis with traditional Global Navigation Satellite Systems (GNSS)-based methods. With the rise of LEO satellite constellations, such as Starlink, LEO-based vehicle localization may offer solutions to GNSS-related challenges. With a large number of satellites and short communication distance, the LEO-based method has great potential to improve accuracy, reduce warm-up time, and provide a robust localization solution for vehicle applications. In this paper, a dedicated LEO satellite simulator is presented, adaptable to various LEO constellations, making it relevant for evolving technologies beyond older LEO systems like Orbcomm or Iridium. The simulator includes satellite trajectory generation, observable satellite identification, and vehicle localization. The LEO simulator was also seamlessly integrated with the Carla simulator for real-time online vehicle localization assessments. Comprehensive tests were conducted with the simulation tools to evaluate LEO satellite-based vehicle localization performance across different satellite counts. Results indicate the potential of LEO satellites for precise and reliable vehicle localization, even in challenging environments. Additionally, the discussion revolves around integrating diverse GNSS-based methods into the LEO simulator, offering a versatile platform for hybrid satellite-based localization research. This study underscores the promise of LEO satellites in enhancing vehicle localization accuracy and stability, contributing to autonomous driving technology and safety advancements.