We compare two Monte Carlo (MC) procedures, sequential importance sampling (SIS) and Markov chain Monte Carlo (MCMC), for making Bayesian inferences about the unknown states and parameters of state-space models for animal populations. The procedures were applied to both simulated and real pup count data for the British grey seal metapopulation, as well as to simulated data for a Chinook salmon population. The MCMC implementation was based on tailor-made proposal distributions combined with analytical integration of some of the states and parameters. SIS was implemented in a more generic fashion. For the same computing time MCMC tended to yield posterior distributions with less MC variation across different runs of the algorithm than the SIS implementation with the exception in the seal model of some states and one of the parameters that mixed quite slowly. The efficiency of the SIS sampler greatly increased by analytically integrating out unknown parameters in the observation model. We consider that a careful implementation of MCMC for cases where data are informative relative to the priors sets the gold standard, but that SIS samplers are a viable alternative that can be programmed more quickly. Our SIS implementation is particularly competitive in situations where the data are relatively uninformative; in other cases, SIS may require substantially more computer power than an efficient implementation of MCMC to achieve the same level of MC error.