In an academic context, which is a "higher" title: "Professor" or "Dr."?

[muon2]

Perhaps it depends on which academic context one is looking at at US institutions.

From the point of view of the student, anyone teaching who isn't a grad student will generally be called a professor, regardless of the degree held. Some grad students can even get that distinction as well, but some don't depending on the nature of the class and the knowledge of the student. Dr. would be reserved for those with that degree. so Dr. might be seen as higher.

A frequent case is when a class may have multiple sections under a single faculty member, and that's the name the student sees - that's the professor. An instructor in the section is then usually not referred to as the professor, but still could be Dr. suchandsuch if appropriate. That would make professor more important than Dr.

From the point of view of the faculty there is a hierarchy of academic ranks. Teaching assistant, instructor, assistant professor, associate professor, and full professor. Some of the full professors may also have endowed positions, but usually all full professors count as the same rank. Dr. is usually held by most of the permanent faculty, so saying someone holds the rank of professor is clearly superior to just Dr.

Then there's the point of view of the support staff. They usually don't want to keep track of academic ranks, so they only use professor when directing students about who they should speak with, as in "Go talk to your professor." When the staff addresses the faculty they use Dr. whenever appropriate. Dr. is the most substantive title in this case.

It is different in Europe. I recall going to a conference in Switzerland and at my hotel they seemed very impressed that I was both a PhD and professor (even at a rank below full) and took to calling me Herr Doktor Professor. So context is everything with titles.