I have a bachelor's in CE, but never had a reason to get a masters. Undergrad in-major courses were a mix of regular high level software stuff, but not compilers and things, lightweight software engineering courses about process and awareness of formal methods (in depth formal methods in the Software Engineering major), some embedded systems work, and then a bit of electrical engineering: IIRC, we did some basic chip layout but my school didn't have any fab resources so no practical work there. A little bit of FPGA stuff.
With that degree, I just write software, mostly for servers, at Internet companies. I don't build hardware or anything, but maybe I'd be prepared for an entry level job in hardware, probably get roped into doing drivers though.