Training two Hidden markov models vs two state Hidden Markov models

I have a scenario where I have log of events followed by some kind of special event (e.g Failure etc). I have two kind of sequences (events, that are observations, can be common in both sequence), one that lead to special event(e.g failure) and one that doesnt. Given a sequence, I want to predict that if it will lead to special event or not(i.e will failure occur or not).

From some papers and answers here and some papers, I came to know that it can be done by training two HMM and predict likelihood of new sequences from both models and select the one which gives maximum, hence the label.

With the actual hidden markov model approach I knew, I thought to have two hidden states (failure and normal) and will train one model. I am reading papers and tutorials for over two weeks but still have confusion that whats the principle between choosing the between these two approaches (summarised again below). There is another answer, from same author, that discourages to use separate HMMs due to fact the sequences are independent, will it also be discourage in my scenario as well and what does independence means in sequence of events?

Data example

normal sequences:
S1 = {e1,e2,e1,e1,e1,e3,e4,e1}
S2 = {e2,e3,e1,e2,e1,e3,e4,e4}