I believe that a static group dungeon grinding might be way more fast than actual FATE grinding iIf the group knows the dungeon.

The difference is that you are committed to 30-60mn of your time, not going afk, autofollow etc... if you want it to be very effective.

Either create your group, there is a tool now to create a party in your server or you can use Duty finder for dungeons while doing FATEs until dungeon pops