Eh, I never liked the idea of Fierce Diety being a version of Link trapped in a mask. Personally I always felt that Fiece Diety was a Moon God that was trapped in the Mask. Unlike Majora it doesn't have a will of it's own. Majora seems like some sort of Sun God that was brought into the mask through the hexing ritual s in which the ancient tribe used the mask in - so literally the mask didn't seal Majora - it's more like Majora possessed the mask.
Plus Majora's Mask just so happened to subconsciously attempted crashing the moon into Termina, I believe he did this for two reasons. One, being a spirit of chaos of course he'd want mass destruction. Two, and probably more interesting - he is using the moon to destroy Termina which will also destroy the moon. What is the anti-thesis of the sun? The moon. Fierce Diety and Majora are complete opposites. Also the Fierce Diety Mask just so happens to be found inside the Moon.
The reason people believe that Fierce Diety is some past incarnation of Link is because in beta versions of MM the mask was simply going to let Link grow older, but the idea eventually was scrapped.