The paper directly compares two versions of a medical speech translation system, one with a grammar based language model (GLM) recognizer and the other with a statistical language model (SLM) recognizer. We construct the GLM using a corpus-based method, so that both the GLM and the SLM can be derived from the same corpus; evaluation is carried out with respect to performance on the speech translation task. Despite using a very small training set for both the GLM and the SLM, the SLM delivers much better word error rates on unseen test material. Nonetheless, evaluating both systems on translation performance rather than word error rates, the GLM-based version of the system outperforms the SLM on the actual translation task.