No.

We know they are very similar in some aspects but can't tell what sets them apart. But we do know there are differences, even if it isn't just the fact Twelve are the Enlightened counterpart. We will have our answer in Heavensward as the Ascian lay the way for Ishgard to summon Halone.

If it hasn't been mentioned yet, I draw attention to the rather peculiar fact the Twelve speak with the living even when they aren't summoned. This was shown in the bonding quests.