The error intensity models for the ML estimation of a signal parameter have been developed in a companion paper [1]. While the methods described in [1] are applicable to any estimation problem with continuous parameters, our main application in this paper is the time delay estimation, and comparisons among the models derived in [1] (i.e. LC, LM, and ALM models)have been made. We first consider the case where only additive Gaussian noise is involved, and then the shot noise environment where coherent impulsive noise is also involved in addition to the Gaussian noise. We compare the models in terms of the probability of error, MSE(Mean Squared Error), and the computational complexity, which are the most important performance criteria in the analysis of parameter estimation. In conclusion, the ALM model turned out to be the most adequate model of all from the viewpoints of the criteria mentioned above.