I agree with Dan Smith. Supper "feels" less formal. As a child, I used supper more. As an adult I use dinner 90 percent of the time, even for "less formal" meals.

I use both. I use "supper" for a normal evening meal at home with family. If I am cooking, I tell my wife I am "fixing supper." I use "dinner" for a fancier, or bigger meal. If we go to a restaurant we are "going out for dinner." If we are inviting guests to our house we are "having guests for dinner." The big celebration meals at Thanksgiving and Christmas, usually in the mid-afternoon, are "Thanksgiving dinner" and "Christmas dinner."