Fates are without doubt the fastest way to level, but also the most boring. And during peak Fate-grind hours (weekends and weekday evenings) it is often difficult to achieve 'gold' (get the maximum exp reward) as a CNJ until you get Holy ability at level 45. Jumping into a fate group is definitely preferred as you'll get credit for killing mobs by healing people in the party as opposed to trying to get credit by tabbing and applying aero to everything.

I don't believe that GC hunt logs give exp.