The Common Core
Both EE and CpE majors will complete the same (common) core of classes.
Both degree programs follow a common core of physics, mathematics, statistics, chemistry, digital electronics, linear circuits, electronics, and introduction to computer programming.
After finishing either program you will have received an introduction to computer programming and data structures, and you will have built a solid foundation of mathematics, statistics and probability, physics, and chemistry. You will have completed three courses in circuit design, a course in linear system theory and signal processing, and will have completed a significant engineering project as a part of the Capstone course.
If you choose CpE, you will receive additional training in computer programming, computer architecture and organization, and networking. The technical electives you will likely take will have further focus on digital computing systems, the circuits that go into them, and the software that runs on them. If you take technical elective courses outside the department, they will likely come from Computer Science (CS).
If you choose EE, you will receive additional mathematics training. Your studies will focus on electromagnetics (electromagnetic waves) followed by a variety of topics such as control system theory, communication theory, advanced analog electronic circuits, and advanced electromagnetics (including antennas and fiber optics). If you take technical elective courses outside the department, they will likely come from Physics or possibly Mechanical Engineering.
As you can see from this description, after receiving the foundation, Computer Engineers focus to a large extent on using that foundation to help them design and analyze digital computing systems. These systems might consist of custom digital circuits to perform some task, or they might be software-programmable computing systems consisting of digital circuits combined with software.
In contrast, after receiving the same foundation, Electrical Engineers focus less on digital or computing systems and more on other topics including electronic circuits, electromagnetics, optics, signal processing, and semiconductors.
All of these sub-topics are important in their own right. The choice of which to pursue largely comes down to your interests.