One thing that often helps me as I think about how to solve a confusing and ambiguous problem is I try to think of the end state, or ideal end of the process.
For example, if your goal is to be a footwear designer at Nike, then a mixed design/engineering degree would not be as helpful as a strict design degree (exceptions apply of course).
If your goal is to design medical devices, then a mixed degree could be very beneficial as often solutions can be highly mechanical (again, exceptions apply)
The first question to answer is what do you want to do after school. Once you have an idea of what that goal is, you can better answer the question of what type of program you want to learn from.