Depending on what level you are, FATE's are not as efficient at leveling as PotD.
PotD floor 51-60 xp scales based on what level you are. For example, at character level 49, each completion of floors 51-60 gives 255780 xp. Compared to Northern Thanalan FATEs which provide between 14,210 and 53,287 for the Gorgimaera FATE, with most giving ~21,315 xp. That means it takes ~12-14 FATEs to equal one run through PotD. A good run through PotD takes ~15 minutes or less. Most FATEs take longer than 1 minute.
And the higher level you go, the better the xp gets from PotD. At Level 52, xp per 51-60 run is 475,200. FATEs in Coerthas Western Highlands average ~15-16,000 xp. That's close to 30 FATE's per level. Dravanian Forelands FATE's average ~24-25,000 xp making it ~19 FATEs per level.
Coupled with the frenzy and focus you have to have in a FATE group to ensure you get to the FATE in time to tag mobs and get credit, and assuming the zone even has a mob of people doing the FATEs to make them take such a short time, PotD easily out paces FATEs as far as efficient leveling is concerned. It's not even a contest IMO given how much "harder" you have to work in a FATE group vs a PotD run. Neither is hard, but one takes more focus and effort than the other for maybe the same efficiency, if not slightly less.
Sources for the information I was using to make these comparisons:
https://docs.google.com/spreadsheets...gid=2137694813
https://ffxiv.consolegameswiki.com/wiki/List_of_FATEs