In this paper two nonlinear observers for a chaotic system are compared. Moreover, the left invertible problem and the observability singularity are discussed. Thus, after a presentation of both observers, a comparison of the two proposed methods and a discussion are done on the basis of simulations results. The last part highlights the fact that the finite time observer is more sensible to the singularity observations, but less sensible to parameter uncertainties and noise in the output of the system.