CompE and CS degree may or may not be similar depends on what major elective courses you choose to take.
For CompE degree program, you can choose your major elective courses in either CompE courses or CS courses. But you will have way more depth understanding in hardware with CompE since you will learn microelectronic (transistor such as MOSFET, BJT), VLSI, efficient machine level coding, and FPGA.
It's easier to finish CS major after you complete CompE degree since if you have taken CompE major elective as CS upper level courses, you get rid of most of CS major requirement. Also lots of Computer engineer courses requirement overlaps with Computer science degree requirement. But if you finished CS major and start to take CompE courses, you would have to take begining core courses for CompE which you would have to take one after another (prerequisite courses). Least that's how it is at Georgia Tech.
There are benefit of having both degrees. For example, the current multicore processor require to utilize not just one core. Having knowledge of interconnect amongst processor, ram and graphic card, you can program more efficiently by knowing how to parallel program. But as master student in CS program, CompE courses helped abit but not as much as I thought it would. Just find out whether you like programing or hardware and go for one of two majors.
I would suggest get master degree instead of double major. You will increase your salary by having master degree than double majors in long run.