A computer engineer builds things. A computer scientist thinks about things.
In my field (computer, video and mobile games) the two are virtually indistinguishable after graduation. We hire computer scientists to write code. We hire computer engineers to write code.
In my experience in education (university, college) computer engineers tend to do more real-world project work and computer scientists tend to focus more on theory and algorithms.
If you are interested in developing new theories and algorithms consider Computer Science. If you are interested in making products (software, hardware, etc.) consider Computer Engineering.