I assume you have the estimated parameters in his model so that given a data point you can make a prediction. Then you could do predictions with both models and compare them. I see no problem with doing this as long as the comparison is meaningful (in this case is the test data set of the type that both models were built to predict.
I am not familiar with mlogit so I cannot tell you if and how you can do it with that particular logistic regression program. But many software products have fit and predict options where if you want to predict a new observation you just supply the model formula.
Aside from that it seems that it would be easy for you to program it yourself by just plugging in the data point to the model formula and computing the predicted logit or through the inverse transformation the predicted probability p.