Tied-mixture HMMs have been proposed as the acoustic model for large-vocabulary continuous speech recognition and have yielded promising results. They share base-distribution and provide more flexibility in choosing the degree of tying than state-clustered HMMs. However, it is unclear which acoustic models to superior to the other under the same training data. Moreover, LBG algorithm and EM algorithm, which are the usual training methods for HMMs, have not been compared. Therefore in this paper, the recognition performance of the respective HMMs and the respective training methods are compared under the same condition. It was found that the number of parameters and the word error rate for both HMMs are equivalent when the number of codebooks is sufficiently large. It was also found that training method using the LBG algorithm achieves a 90% reduction in training time compared to training method using the EM algorithm, without degradation of recognition accuracy.