In the original Jane Eyre, Jane leaves Rochester because he is married and it goes against her moral fiber to be with a man who is married. When she runs, she does not want him to find her (at least, IMHO.)
When Jane Moore runs it seems to be more because she thinks Nico Rathburn is still in love with his mentally ill wife. It does not seem to be a moral stand about anything, at least, not a strong moral stand. Later, she admits that with all she did to make herself disappear (mails her cell phone to San Fransisco, changes her name) she was still hoping he would find her and convince her to come back. So basically it was just a test of his love for her and in this case, he kinda fails. But HEAs for everyone because this is based off the slightly more optimistic sister's book.
This completely alters the message of the original book for me. Though, for once, Jane has one damn flaw.
Oh, and I meant to tell you that I don't hate all updated versions of classics. I liked "10 things I hate about you." And, well, I'm sure there are others too, some that I probably didn't even realize were updates of something else.