If I recall correctly, the only requirement is that you are not wearing armor and then it gives a straight +3 bonus. This makes it very useful for monks, barbarians and wizards.Don't bracers of defense give you an AC of 13 + Dex bonus?
If so, they won't allow for unarmored defense to work as well; you would have to choose (f'rexample) AC 13 + Dex from bracers or AC 10 + Dex + Con (from barbarian unarmored defense).