Suppose we have constructed a model of some stochastic system; we are also able to perform Monte Carlo simulations of this system. Now, we have two sets of samples: one from our model and one from the MC-based approach, and we would like to assess the accuracy of our technique.
The first two accuracy measures, which come to my mind, are the differences of expectations and variances. Then, one can try to construct the empirical PDFs/CDFs and compare them at certain points, e.g., find the RMSE.
What are the most preferable and exhaustive ways to draw this comparison? Which metrics are the first ones to look at, which are a must?