How many work between a CS major and EE major overlaps in the industry?

The EE/CS field is so broad that your question has no good answer. Your best bet, at the undergraduate level, is to become good at the basics and theory. If you want to get into chip design, a good background in physics, chemistry, and mathematics is vital.

The choice of school is also relevant. Some schools think CS means the internet, others think it means programming. With Microcontrollers much of the work consists of using technologies and hooking them up rather than designing them and some good EEs become bad programmers while some CS folks don't understand what happens with high frequency signals.

If you want to make a difference in the industry you might want to go on to the Master's or PhD level, thus my suggestion on the basics. Other career paths for an EE might lead into sales and administration.

Regardless these days the most important skills involve working in a group and good written and verbal communications are vital. Extracurricular activities such as sports and clubs add to your portfolio and a good understand of history and psychology will help you.