As an employer I would worry that a graduate does not have real world experience having been protected in education for so long. So I would be keen to see evidence of having done some work experience, paid or unpaid in different areas.
I think that the fact that they have managed to get a degree should show that they are able to get fully involved in complicated tasks and see them through to the end. It shows that they have the will and desire to succeed, which is something that would stand out when compared with those who are not graduates.
Graduates should be more capable of doing a job, because of the extra study that they have done. Make sure that you demonstrate in interviews, that your education has been worthwhile and given you skills that you will be able to use in the job.