Square let us redo quests on different classes.

[Voltyblast]

I was in though that repeatable quests are called levequests and are giving exp on par with FATEs (and even more sometimes).

I'm not entirely sure considering that I was checking leves a moment ago, and level 58 leves give 25k while azys FATEs give me about 58k+ or something. I might be wrong though and probably checked badly, so I'll leave it be for now.
However my issue is, considering the time it takes time to do a levequest you might as well do a FATE: it's 1-2 (or more) minutes against 30 seconds from a fate (whether in group or not). Quantity over quality I'd say.

Besides, doing quests is more fun than doing repetive levequest and FATes (plus the exp reward aren't bad at all) and, correct me if I'm wrong, this is a videogame. Y'know, it's supposed to be enjoyable and fun, not boring and tedious and while fun and boring are subjective things, I don't really see the problem of "refreshing" the quest on class switch. I only see win-win here.

If not, well I guess I'll stick with dungeons: FATE groups are so few and I rather save leves for gathering and crafting.