AIC, BIC, and some pseudo r-square measures are based on the log likelihood and the number of terms and observations in the model. If you are able to extract the log likelihood from a model, these statistics can be calculated.
Sometimes AIC etc. are expressed in terms of deviance instead of log likelihood.
If the model is nested model you log likelihood is preferable unless AIC and BIC are preferable criteria. Caution: Don't use log likelihood to compare the models if the model is not nested models.