I started studying ME last year, but changed to ID this fall.
Personally, I’m very satisfied with the choice and having a lot of fun. However, this is a choice you have to make yourself. Are you interested in making an already conceived product work? Or would you rather create your own designs/inventions from your imagination?
Many ID degrees also include a couple of engineering courses such as mechanics, material technology and production technology.
Don’t think too much about money. It is impossible to know the job market four or five years from now. Far more important it is, to study something you enjoy, because then you can become really good at it. And skilled people always get jobs.
No one says it better than Alan Watts: