EE is Electrical Engineering, if you like pure circuits and signals and enjoy long hours working in labs testing and calculating currents, voltage, etc. (btw if you hate physics, don't go for either EE or CompE, you will regret it later on!!) then you should go for EE, job market for EE is pretty good right now, with your B.E.E. degree, you will probably have a starting salary of around $45,000/yr.
CompE is Computer Engineering, to get a B.C.E. degree, you have to take EE courses as well as CS courses, so you need to know both circuits, signals and programming, computer design. If you enjoy studying digital logic, then you should go for CompE. Salary for CompE is about the same as for EE.
CS is Computer Science, what you study are programming in various languages, learning different data structures and algorthims, learn how to debug, methods of object oriented programming, etc. if you like spending long hours programming, then go for CS. The starting salary for CS major is about $40,000/yr.