Nerseus is right on, I have never been asked for my resume, as I work mainly on contracts, although employers do ask for resumes.
They really care more for experience (work history) more than a diploma. But as Nerseus mentioned, if you have no work experience then all you can have in your favor is a diploma.
Basically, if they were to choose between a person with 3 years of school and another with 3 years of work experience, they will pick the latter.