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Wheel slip control is crucial to active safety control systems such as Traction Control System (TCS) and Anti-lock Braking System (ABS) that ensure vehicle safety by maintaining the wheel slip in a stable region. For this reason, a wide variety of control methods has been implemented by both researchers and in the industry. Moreover, the use of new electro-hydraulic or electro-mechanical brakes, and in-wheel electric motors allow for a more precise wheel slip control, which should further improve the vehicle dynamics and safety. In this paper, we compare two methods for wheel slip control: a loop-shaping Youla parametrization method, and a sliding mode control method. Each controller is designed based on a simple single wheel system. The benefits and drawbacks of both methods are addressed. Finally, the performance and stability robustness of each controller is evaluated based on several metrics in a simulation using a high-fidelity vehicle model with several driving scenarios.