I know good Electrical Engineers with degrees in Physics, and I know good Physicists with degrees in Chemistry. It's what you know and what you do that really matters, IMO. Granted, if your degree is in History, people will assume you don't know much Physics.
My undergrad is in "Engineering and Applied Science". If you asked me to build a bridge or a refinery, the results would be scary. What I did was electronics and no one cared that it was called "Engineering".