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

[King of Kensington]

Is it true that even the lowliest adjunct (many but no means all of which hold doctorates) in the US can still be properly be called "Professor X"?

That's not the case in Canada or the UK though.  In the UK, it's only the equivalent of distinguished professors in America who get the title.  In Canada, tenure-track and tenured faculty can be called "Prof. X" but below that they're called lecturers or instructors and don't go by "Professor."

It seems that the Canadian/British/European approach makes more logical sense, since most professors hold doctorates but most doctorates aren't professors.

[King of Kensington]

Yeah, about 2% of Americans have a Ph.D. or a professional degree like the M.D. that allows them to have the title Doctor.   Far less than that are tenured or tenure-track university faculty.

So yes, well it is of course accurate (and perfectly correct) to call a full-time faculty member with a Ph.D. either Dr. or Professor it seems that Professor is the "higher" title to me. 

In the end, most doctorate holders are not professors but most professors have doctorates.

[King of Kensington]

According to the BLS, 44% of postsecondary teachers have a doctoral degree, but this figure includes vocational teachers, graduate student TAs etc.

https://www.bls.gov/emp/ep_table_111.htm

According to AAUP, 67% of full-time professors have a PhD or first professional degree:

https://www.aaup.org/article/characteristics-full-and-part-time-faculty#.WHpX9hsrI2w

[King of Kensington]

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

Professor, certainly.

I became Doctor angus the day I got my PhD, but it would be many years before I would become a Professor.  This is the case for most of my colleagues, who all did post-doctoral fellowships either with the government or universities, and sometimes in the private sector, for anywhere from two to four years. 

All the members of my department have PhD degrees, including all the adjunct professors.  This is true for all the departments in my university except in those cases in which the terminal degree in that field is not a PhD.  (There are also MD, EdD, ThD, DSC, etc., and some only have MS or MA degrees, but that's rare and limited to a few fields.)

I remember when I first started graduate school I asked my mentor whether I should call him Professor or Doctor, and he said, "Call me Dennis.  But if you must be awkward and formal, then call me Professor because I have earned it."  He, too, did several years of post-doctoral research after he got his PhD before becoming a member of the faculty.

That said, students don't always observe such rituals.  We are not very formal in the US.  I worked in Amsterdam for a while, and went to school in Germany as well, and I noticed that they are much more formal over there.  Also, I've been at conferences where there are Japanese and they are much, much more formal.  I've seen post-docs bowing and scraping before their professors.  We generally are on first-names bases with our faculty mentors when we are grad students and post-docs.  Also, students just call everybody Doctor Something without checking to see whether they are actually more appropriately called Professor.  I don't know any US professor who gets hung up on that sort of thing, though. 

But if someone actually has the title of Professor and you insist on being formal, then use that because it is "higher" than Doctor, and they would have had to jump through additional hoops after obtaining the doctoral degree to be appointed to a position that carries the title Professor.

This makes sense.

Of course it would not be wrong to call a full professor with a Ph.D. either (and usually grad students in the anglosphere are on a first-name basis with their professors). 

[King of Kensington]

I once shared an office (no Ph.D. yet) and on the door the person the label for either a previous user or the person I was sharing it with was marked PROFESSOR X Y.  She (or maybe someone else in the office) crossed it off and marked in "Dr."

I don't know if she was doing this to "elevate" her status (hey I'm a Dr. now, not "just" a professor) or because it was a mistake and she didn't want to use a title she hadn't yet obtained.

I should say the tenured faculty office doors all say "PROFESSOR" next to their names.