Looking at it in a storyline view. Don't forget the "Devivification" Abysseans suffer for traversing to Vana'diel.
Quote Originally Posted by http://wiki.ffxiclopedia.org/wiki/A_Goldstruck_Gigas/Plot_Details
Ragemont: In crossing over to this world, residents of Abyssea suffer from a phenomenon wherein their strength is halved.
"Devivification," 'tis called, though the exact science of it remains beyond our fathoming.
The idea of alternate Phoenixes and Bahamuts and their "strength" being halved doesn't appeal to me.