Depends on what you want to do.
Generally:
Computer Science is for doing software - writing applications like Microsoft Word or Firefox. It's mostly high-level stuff and focuses on application-level software, on the design process, and on user interface design.
Computer Engineering is lower-level stuff - writing the BIOS software on a PC, programming microcontrollers. Computer Engineering also encompasses some parts of Electrical Engineering - it includes designing and building circuitry to interface with microcontrollers, or studying the design of the microcontrollers themselves.