HMMs are generative models of sequences, so you can use pretty standard methods to compute and compare likelihoods.

For your third sequence, you can compute the likelihood of observing the sequence with each HMM, and compare the two likelihoods to find the best model.

For comparing the two HMMs, I would combine your two sets of sequences and train a single shared HMM off of that unified dataset.Then, you can calculate the likelihood of the data using that null model and also the alternative of two separate models. You can then use a likelihood ratio test to judge significance.In other words, you want to see if two separate models fit the data much better than a single shared model. If a single shared model is almost as good, then the two models are not significantly different.