Not sure if this is true where you are, but in the US the difference is can be viewed as applied science versus pure science.
Comp sci leans toward the theoretical aspects of computers and computer software. Electrical and electronics engineering, on the other hand, are almost entirely practical, involved in the design and manufacture of hardware and software.
You have to decide which one you are more comfortable with and what your future goals are. Multiple degrees are good if you are going to teach or work in administration/management. If you are looking to do hands-on work, then you need to focus on a particular discipline. Experience becomes much more important than advanced or multiple degrees in that case, other than maybe a masters specific to a particular field.