Dual citizenship, papers necessary for employment. (Vienna)

Hi there,
I am an American with dual citizenship. I understand this will make it easier for me to find employment since I don't need a work visa but here is my question. I have a European passport ( as well as USA) will that European passport be proof of my ability to work or will I need additional paperwork, etc??I would appreciate some guidance from someone who was at one time in similar circumstances. I want to be able to say to a prospective employer that I don't need a visa and because I am not married or have children, transitioning to Europe to work should not be difficult.