Classes are jacks of all trades, have no major defining abilities that the other classes can't use etc - allowing flexibility.

Advanced jobs have a more defining role. Have advanced job abilities which are usually found in FF lore as fairly specific abilities (such as DRG's iconic Jump, WHM's regen, etc).

I feel classes are more like a baby step before you can truly become a legendary "Dragoon" or "White Mage" as an example. You have to train as a weak Gladiator before you can be regarded an almighty Paladin. Just makes more sense, battle mechanics aside to be honest.