Two of the most advanced procedures for recursively estimating the parameters in linear, observation space models of stochastic dynamic systems are the prediction error (PE) and optimal generalized equation error (OGEE) methods. This paper discusses the relationship between these methods in the case of the transfer function (TF) or Box-Jenkins model ; and compares their performance in terms of optimality, computational complexity and practical robustness. While the methods are quite similar for the TF model, it is shown that the instrumental-variable inspired OGEE approach yields algorithms that are computationally simpler and more robust when applied in practical situations.