I started out as a CE major, hated the EE prof at my small college and went CS. I continued to do the non-EE CE classes though - digital design and whatnot (learning how to make a full adder, reduce complexity and such, in the second class it was put to use, with FPGAs and simpler microprocessors/controllers like a 8086 and an 80251.)
Now, I work at a large Software company...and honestly, the CE stuff helped me in that it made me learn assembly, and learn it well...but I also did that in Compiler Design. If your goal does not involve EE work, then I'd say skip CE. CE is a TON of work compared to a straight EE or CS major as every CE program I've seen is quite literally EE and CS majors combined, with only one or two requirements removed. It can easily become a 5 year major.
My advice, is make sure your college makes you do projects - designing, implementing, testing...and also make sure your college teaches some amount of C code, and assembly. Compiler design is quite frankly the best course I took. Not too long later I had an internship working on BluRay and HD DVD players where I was reading through assembly and changing values in the registers on a MIPSII system.