I don't see anyone here from the comp eng. POV.
The first thing to ask about microprocessor design is: where do you want to go with it? I don't think that there are many jobs in Oz.
I like to think that comp eng gives you the whole picture. When you run that app on your pc, do you want to know whats in the .exe? how it's loaded into mem? how the os schedules it? how it gets run in the cpu? how the cpu works (down to the transistors)? While all of this could be considered theoretical, and "doesn't matter" when you are writing large apps in a performance critical environment I find it really useful to know what happens underneath the compiler.
That's what comp eng gives you. There's also at least 1 seng course in the core of comp eng - so you don't miss out on the docs planning etc. entirely. Even if you start off doing cowboy style programming - by the time you've dealt with a couple of 10kloc OS's and other large apps, the benefit of planning will become really obvious. And, speaking from experience (know that I'm finished) it's really annoying when people don't plan their programs at work. I spend a few mins doing it, and finish with a much better product.
Elec eng is really hardcore electronics, physics and maths, compared to what you get in comp eng.