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The acoustic models of conventional state-of-the-art speech recognition systems use generative Gaussian HMMs. In the past few years, discriminative models like for example Conditional Random Fields (CRFs) have been proposed to refine the acoustic models. CRFs directly model the class posteriors, the quantities of interest in recognition. CRFs are undirected models, and CRFs do not assume local normalization constraints as HMMs do. This paper addresses the issue to what extent such less restricted models add flexiblity to the model compared with the generative counterpart. This work extends our previous work in that it provides the technical details used for showing the equivalence of Gaussian and log-linear HMMs. The correctness of the proposed equivalence transformation for conditional probabilities is demonstrated on a simple concept tagging task.