Viterbi training vs. Baum-Welch algorithm
From my comment:

This answer on crossvalidate.SE may be of use. I wasn't aware of viterbi-training. I have only used BW or other EM-based methods in the past. Based on the answer in the link, I think BW would be the most useful. It seems Viterbi-Training gives no guarantee on bounds. However, the latter does have useful application if BW takes far too long to compute.