A comparative study is conducted to evaluate three types of lattice Boltzmann equation (LBE) models for fluid flows with finite-sized particles, including the lattice Bhatnagar-Gross-Krook (BGK) model, the model proposed by Ladd [Ladd AJC, J. Fluid Mech., 271, 285-310 (1994); Ladd AJC, J. Fluid Mech., 271, 311-339 (1994)], and the multiple-relaxation-time (MRT) model. The sedimentation of a circular particle in a two-dimensional infinite channel under gravity is used as the first test problem. The numerical results of the three LBE schemes are compared with the theoretical results and existing data. It is found that all of the three LBE schemes yield reasonable results in general, although the BGK scheme and Ladd's scheme give some deviations in some cases. Our results also show that the MRT scheme can achieve a better numerical stability than the other two schemes. Regarding the computational efficiency, it is found that the BGK scheme is the most superior one, while the other two schemes are nearly identical. We also observe that the MRT scheme can unequivocally reduce the viscosity dependence of the wall correction factor in the simulations, which reveals the superior robustness of the MRT scheme. The superiority of the MRT scheme over the other two schemes is also confirmed by the simulation of the sedimentation of an elliptical particle.