(Some engineers move from one field to the other)

1. Please clarify, do you want to "work with hardware ICs", etc., or do you want to actually work on semiconductor fabrication, SOC, ASIC design, etc?

I expect you will probably want to pursue a Masters in EE with a specialty in semiconductor design if the answer is the latter.

If your answer is the former (work with hardware), then personally I would choose CPE, *GIVEN THE INFORMATION YOU HAVE PROVIDED ME*.

Reasoning:
Personally I graduated with a BS in EE with the EE courses, and after deciding embedded systems design is what I desire, I had to, on my own free time, learn:
-Programming for embedded sys. (C, now learning C++)
-Hardware design (some analog, mostly digital, digital logic, and CAD PCB design)
-Real Time Operating Systems (RTOS)
-FPGA design: VHDL/Verilog

So you can see an example: had I chosen CPE courses, if available, I would have been far better prepared already as opposed to graduating with a ‘generic’ EE degree, which was not more specialized.

If you are pursuing ASIC/semiconductor IC design, perhaps someone else can comment on that.