If you can already form an idea of what you want to do or what would fit you best after your school, and formulate it as a long-term goal in a personal development plan of some sort, that would be ideal.
Succinctly put you can see product designers as the people coming up with the ideas and concepts, and the product engineers as the people taking these ideas towards production. In my experience these two disciplines overlap as product engineers can come up with very interesting concepts as well, and need to be involved into the creative process. Concretely, a product engineer will put more time in drawing and designing mechanical features, working out the details in 3D, and communicating with suppliers. I advise to go for a school that, at least in the first years, does not emphasize one too much over the other, unless you already have a specific plan for yourself, but allows you space to develop in a lot of different areas of design while getting good personal coaching/tutoring.