Appropriate "title" to list on application for professors writing LOR?
"Professor" is in some respects a more "advanced" title because many people who have doctorates are not professors. You may have writers who have a doctorate, but do not hold a professorship. 

I would put "Professor," but in most places, it does not matter at all. (I've read that Germany for example is a stickler for titles, though.)

It would not be typical to include "Professor of [X]."