You design a Curriculum Vitae to give to the employer a BIGGER PICTURE of you as student, as a person (interests and achivements) and as a worker, it's a wider information. A resume is really brief and, generally, just goes to the point without showing too much background. I suggest you to do both, a CV is a time consumer and sometimes a pain... you know where... but it's necessary to do an efficient resume because you will know exactly how to "condense" de information in a adequate way.
Once you have both... you could "play" with them in order to know which one you need in different situations... and if someday you are not sure of what you can send, send them both !!! you can always put your resume in front of the curriculum vitae.
^^