Network autocorrelation models for count and rate data have received little focus in the literature. In this paper, we develop and compare three network autocorrelation models for counts and rates when the peer effect (also referred as social influence or contagion) is specified on the conditional mean of the outcome determined under Poisson, negative binomial, and generalized Poisson outcome distributions. We compare the three proposed models and the performance of their associated Bayesian estimation procedures for the model parameters through a comprehensive simulation study.