I have a Computer Engineering degree. When I explain what it is to people I say that it is basically an Electrical Engineering degree with a Computer Science minor. Both degrees were from the Electrical Engineering department and at the time there were only six classes difference between EE and CP (computer engineering). A lot of people got a double degree rather than getting a Masters in one or the other. On the other hand Computer Science is not an engineering degree and was run by the math department. There is almost no overlap in classes. For instance, when I took chemistry, physics and statics/dynamics classes; I took them with the chemistry, physics and mechanical engineering majors. Computer Science also took chemistry and physics but at a much more remedial level similar to the honors level classes I had in high school.
Nothing wrong with Computer Science, but if the kid has the aptitude I would definitely suggest Computer Engineering as not only a better education, but to open more doors. Sure they might end up programming for a business and not need the science background, but who knows? Might end up designing robotics or something and really need the engineering background not only to pass the interview.
I work as a contractor for NASA and hire entry level engineers every year straight out of college. I have never hired a Computer Science major for one simple reason: NASA won't let me. They have a list of accepted degrees and CS is not one of them even with a Masters. We hire Electrical, Computer, Mechanical and Aerospace Engineers predominately.