Multinomial logistic regression

I have been carrying out some analysis using multinomial logistic regression and I would like to compare two competing models to see which is the best. I have examined the Cox & Snell and Nagelkerke statistics as well as the overall classification percent correct and the AIC, however, I want to know if I can test the difference between these models.

Can anyone help?? pretty please!!
It's a bit complicated - I've got two models that I want to compare that don't have the same predictors but also two other models (which I also want to compare) where only one of the predictors is shared.

It's been suggested that I should be using SEM to compare them - do you know of another way or is this the best solution?

Any help greatly appreciated!