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This paper presents a comparative study of adaptive control approaches for Micro-Electro-Mechanical Systems (MEMS) z-axis gyroscope, adaptive controller and adaptive sliding mode controller are proposed respectively and compared in the simulation. The proposed adaptive control approaches can estimate the angular velocity and the damping and stiffness coefficients including the coupling terms due to the fabrication imperfection. The stability of the closed-loop systems are established with the proposed adaptive control strategies. Numerical simulations are investigated to verify the effectiveness of the proposed control schemes. It is shown that adaptive sliding mode control has better robustness in the presence of model uncertainties and external disturbance than adaptive control.