FATEs is fastest, but I recommend to queue for dungeons and FATEing while waiting to get the Gil and equipment to make your leveling go around economically if you care for in game economy. Trust me, most of the time you will still be FATEing even if you queue for dungeons. Atleast if you are leveling a DPS.

If you do not care for neighter fun or economy and just want your XP FATEing is the way to go.