I have training data that I have fitted with two types of Poisson models (one zero inflated and one standard) and I would like to compare each model's performance on a test set to see which one is better. How can I do this ? (I am using R if it makes a difference). I have already done chi-squared tests to determine that both fitted Poisson distributions are statistically significant with the training data.

Also, is there a standard way for testing the accuracy of a fitted probability distribution on a test set of data? E.g. like a mean-squared error reduction.