In very broad terms, Computer Engineering is about hardware, and Computer Science is about software. Each cannot exist without the other, and the coursework will overlap heavily, but the focus is different. Do you want to build processors, logic circuits, and feedback loops? That's computer engineering. Do you want to understand logic, learn about how to make those processors really dance, and layer software on top of all that hardware? That's computer science.
Really, either of these two degrees (and others) opens you up to major sections of the design, technology, and consulting job markets. The mobile device revolution is keeping demand for new processors, memory, and other integrated circuits very, very high, and there's always, always, always a demand for people who can code. You cannot go wrong. Both degree paths will at some point require that you choose something to focus on - a specific language or set of languages to program in, a certain target industry to develop machines for, etc, so it's best to work backwards from what you think you might want to do, or what you're interested in. Want to make video games? Computer science, all the way. Interested in building computers? Computer engineering.
You can also expect that the first three semesters (at least) will have a lot of overlap in terms of base classes. Calculus, Differential Equations, Logic and Design, Intro to Programming, etc will be required in both degree plans. So if you continue to grow and learn more (as we all should be doing!), you can change your mind.
The career prospects for both are incredibly strong. I can't speak to all universities, but here's some detail for the University of Texas in Austin. I'm BSEE Computer Engineering from UT, 2001, btw.
- Department of Electrical and Computer Engineering - http://www.ece.utexas.edu
- Department of Computer Science - https://www.cs.utexas.edu/