In my career so far developing software for chemistry I've made heavy use of graph theory, formal language theory, and data structures that I learned while an undergraduate.
I don't have the same assessment as you in the advantage of a CE degree over a CS degree. I suspect there's a bias error, as you did not enter a field where a CS degree would have been more useful. Nor do I think that a CS degree is specializing, given the courses I took in operating systems, programming language theory, computer graphics, databases, etc. Of course, from my perspective "electrical design, hardware/chip design, embedded systems design" are all variations of the same thing, so it's a definite matter of perspective.
In any case, after 5 years or so in a career, the specific advantages of one background over the other get pretty weak.