It seems to be apparent that you, O my daughter, are from the khalaeej (the Gulf States) if in fact you are not from Saudi Arabia. It is obligatory upon the Muslim woman to wear the Jilbaab. The jilbaab is an outer covering that conceals the beauty of a woman and her clothing; it covers her body from head to toe. This means that it covers the entire body.
As for the 'abaaya that is most popular in the Gulf States, then it has taken the place of the Jilbaab.
I say that if in your area the jilbaab is predominately worn by the people, then do not wear the 'abaaya. However, if in your area or country the people predominately wear the 'abaaya then do not obey your parents (i.e. wear the Jilbaab not the 'abayaa) as there is no obedience to the creation when it involves disobedience to the creator.
At this point I would like to clarify that the 'abaaya of the woman is be worn upon the head, and for her to wear it upon the shoulders is an error, even if some of the people of knowledge have given verdicts that the 'abaaya can be worn on the shoulders.
Verily, those who have given the verdict (stating) that a woman can wear the 'abayaa on the shoulders have only done so because they were unaware that the 'abayaa has taken the place of the jilbaab; and the Jilbaab is worn from the head.
Understand this, may Allaah bless you.