I use DirectoryPress, which is a WordPress theme, for my directory of directories. For a directory with a limited scope, like mine, it works fine, but I would not choose it for a larger directory, at least not unless I'm very familiar with WordPress. Outside the box, it looks pretty good, and there are many design changes that can be made without modifying the theme itself, but I do not like the way the subcategories are displayed, so I do not use it. in a directory that would have many subcategories on any page, like all cities and towns in a state. I'm sure there are ways to avoid that, but I still have not discovered what they were.
PremiumPress, which makes DirectoryPress promise 24/7 technical support. While you will in fact receive an answer to your questions, this answer will rarely be of any use to you. Mainly, regardless of the problems I had, they replied that I could not do what I wanted with PremiumPress, only to find that someone in their forum could tell me how it could be done.
The impression I got was that DirectoryPress was created by people who understood WordPress, but had little idea of what might be needed in a directory. Therefore, they could not understand why they might want to have the ability to display subcategories in columns instead of randomly on the page. Your technical support staff also does not seem to know much about the product they are supporting.
Like others here, I would recommend eSyndicat, phpLD or another script created by people who understood the directories and the needs of directory operators.