Only you can answer this question because it is asking for your opinion. I can give you my opinion, but how will that help you?
You need to try to think of yourself as someone like Eveline. Your icon is a male figure, so I'll assume that you're a guy. Try to think of yourself as the oldest son in the family. Your father recently died, and you have a couple of younger siblings. Your mother works, but she doesn't earn enough to support the family, so you have to quit school and go to work. It takes all of your income plus what you can get from your mother just to pay the bills and feed everyone.
Now imagine that you have fallen in love with a beautiful young girl who is moving to another state for a job. She begs you to come with her and start a new life with her. The idea of being free from family responsibilities is very appealing to you, but what would they do without you?
Your girlfriend has already boarded the plane, and you are standing in line at the terminal. Do you go or do you stay? Why? That's what Eveline had to decide.
I hope this helps.
There are pros and cons to any decision she made. If she went with Frank, she might have a chance at a life without the abuse of her father. Her thankless servitude makes life a bland existence and in her young life she has many responsibilities. If Frank turned out to be an honest man, she might have a chance at a happy life. But, there are other considerations, as well. Would she be able to over come her guilt at breaking her promise to her mother? Would Frank turn out to be a loser? Is it safe to go off to another country? What options does she have if she is unhappy?
There are no easy answers to your question, which is possibly why the author left it up to the reader to decide what she did.
Eveline's decision to run away with Frank would go against her up bring and what she believed in. She had made promises to a dying mother to keep the family intact. Although, her father was abuse; he was getting old and needed her. Eveline was responsible for two children. Her fear of the unknown life with Frank and the chains of duty kept her from getting on that ship. Eveline chose the familiar.