The community seem to prefer using Palace of the Dead for leveling now which gives fast gains and doesn't have composition req for the queue so you don't need to wait long for tank/heal to join party like you would with regular dungeons. Unlock it from New Gridania from Lv17 and up.

Sidebar: would be nice if levequests could regenerate the allowance faster or have no allowance any more, just uncap. Would only need to adjust the exp gains from DoH leves if it was uncapped. The battle ones still wouldn't be competitive with other exp methods if you could do unlimited.