REML (restricted maximum likelihood) has become the standard method of variance component estimation in animal breeding. Inference in Bayesian animal models is typically based upon Markov chain Monte Carlo (MCMC) methods, which are generally flexible but time-consuming. Recently, a new Bayesian computational method, integrated nested Laplace approximation (INLA), has been introduced for making fast non-sampling-based Bayesian inference for hierarchical latent Gaussian models. This paper is concerned with the comparison of estimates provided by three representative programs (ASReml, WinBUGS and the R package AnimalINLA) of the corresponding methods (REML, MCMC and INLA), with a view to their applicability for the typical animal breeder. Gaussian and binary as well as simulated data were used to assess the relative efficiency of the methods. Analysis of 2319 records of body weight at 35 days of age from a broiler line suggested a purely additive animal model, in which the heritability estimates ranged from 0.31 to 0.34 for the Gaussian trait and from 0.19 to 0.36 for the binary trait, depending on the estimation method. Although in need of further development, AnimalINLA seems a fast program for Bayesian modeling, particularly suitable for the inference of Gaussian traits, while WinBUGS appeared to successfully accommodate a complicated structure between the random effects. However, ASReml remains the best practical choice for the serious animal breeder.