I did Chem engineering in college, but have been programming since I was 17.
Now I've moved to electrical design Engineering since it seems to be a hybrid of engineering and programming.
So far my job is understanding everything that goes into my complex system. I'm not sure if this or embedded programming is my future. What is more valuable?
Traditional engineering skills are very undervalued in this industry and I've met very few "engineers" in this field who understand engineering basics like control systems. IMO that's very valuable for building the systems we build -- I can't tell you how many half-baked implementations of some of the parts of PID I've seen kicking around.
And I say that as a completely self-taught, college dropout senior developer.
In fact, I have a perfect counter example. At reddit, to even out load on our databases, we built a system that would take into account current load on the database when choosing which read slave to select. As it turns out, this doesn't work well, because you overwhelm the slave with the lowest load because the the reaction time is too slow compared to the request time. We had to tweak it to account for this.
Had we known control theory, we would not have made this mistake. On the other hand, that mistake didn't cause us that much damage and we were able to devise a solution that ended up being right. :)
I do a lot of embedded work without a CS degree. Every board and chip is different, so you learn by doing. But,at the same time a lot of hardware is basically the same. You have some low power cpu and a bunch of standard peripherals. Once you know how most of them work, it's just engineering to figure out what libraries you need.
There's lots of work in embedded that's for sure. There's also a huge amount of variety depending how close to the metal you want to be.