The MSQ is an illusion that it is fast. You get large chunks of XP for the MSQ, but with all the running around you have to do, it's not much faster than just running dungeons or doing FATEs.

Dungeons/Daily Roulettes are by far the fastest XP. While you're waiting for a dungeon queue to pop, you can:

-Do FATEs
-Do Levequests
-Do Clan Hunts
-Do Challenge log