This paper presents a comparative study between two methods dedicated to the robust estimation of load torque and flux of induction motors (IM). The developed approaches rely on the adaptive Luenberger observer theory. The first method is based on the development of a Takagi-Sugeno Adaptive Luenberger Observer. In order to enhance the dynamic of the load torque estimation, a second method is presented using a Takagi-Sugeno Fast Adaptive Luenberger Observer approach. Sufficient conditions are presented to ensure the asymptotic convergence of the flux and the load torque estimation errors. Moreover, robustness performances are considered in order to minimize the impact of the rotor resistance variations on the quality of the estimation. Experiments were carried out to illustrate the effectiveness and the robustness of the proposed results and to show the advantages and limitations of each method.