There is a growing recognition that discrete choice models are capable of providing a more realistic picture of route choice behavior. In particular, influential factors other than travel time that are found to affect the choice of route trigger the application of random utility models in the route choice literature. This paper focuses on path-based, logit-type stochastic route choice models, in which several forms of logit-family models have been calibrated using practical data and examined on an illustrative network. For each type of the logit-family models, two modeling approaches have been implemented in stochastic traffic assignment (STA). The first approach is a univariate route choice model. Challenges in the estimation of path utility are discussed and a heuristic estimation algorithm for univariate models is proposed. As the proposed approximate calibration method does not require resorting to choice data, it can be regarded as a more practical method than the traditional approach and can overcome many inherent difficulties in calibration of route choice models in univariate case. The second one includes a multi-criteria path utility function considering travel time and monetary cost along with travelers’ income to determine the equilibrium network flow. This model has been calibrated based on a stated preferences data set. This study showed that estimation of the utility could have remarkable impacts on the equilibrium flow and thereby on policy assessments, while the impact of model specification is far less severe. The importance of this achievement arises from the fact that most of the efforts made in stochastic assignment literature have been dedicated to apply theoretically appealing choice models, and model calibration by comparison, have not received considerable attention.