Since early 1970's, the multinomial logit model has been used in the decision making such as mode choice, location choice housing choice and so on. However, there exists an debate regarding the specification of parameters in the utility function. One approach is to define the parameters to be alternative-dependent. Therefore the number of vector of parameters equals the number of alternatives subtracting by one. This approach is refered as the original multinomial logit (OMNL) model in this study. Another approach is to define the parameters to be the common marginal effects of variables. Hence, there is always only one set of estimated parameters no matter how many alternatives are in the choice set. We refered this approach as the general multinomial logit (GMNL) model. In this study, we compare these two models from the theoretical fundation, calibration problems and model interpretation. It can be concluded that these two models are identical in binary choice. The OMNL model is theoretically better in current behavior interpretation and the GMNL is favor of estimating the probability of new alternatives.