Selected answers from the Dumb SEO Questions G+ community.
Ewald van der Hoop: Has a .directory TLD any benefits over a CcTLD for a directory website?
Jim Munro: Until some who knows what they are talking about comes along, Ewald, I am going to say no difference whatsoever.
Ewald van der Hoop: Thanks, Jim. No difference is good, as a CcTLD might normal be the best choice. ;-)
Pe lagic: A non-geotargeted GTLD will have a slight advantage over a CcTLD for global queries, and a slight disadvantage for a country's specific queries.
You could have also asked if .directory TLDs have any benefits over the established GTLDs, in which case the answer would be as ;pointed out, ;no difference whatsoever.
For GTLDs, using G's Webmaster Tools, you can either set a geotarget, or disable G's auto-geotargeting (unlisted). If you were to set it to a particular country, then compared to a CcTLD, again it would make no difference.