The difference lies in the assumption you do for distribution of the error term (is it normal? -> Probit, is it logistic? -> logit).
Actually, for non-extreme values the results (meaning, the forecasts) are very very similar. Even more, there is a quite robust numerical relationship between the estimates with a probit and a logit model.
Thank you, I thought it was enough to determine the largest value of the log likelihood obtained by each model. This is based on the objectives of the maximum likelihood method.