If:
Your Chocobo reaches Rank 10 in one tree, you can re-spec it and claim the barding of the second tree (Because you have not yet claimed the barding from the NPC)
However:
Your Chocobo reaches Rank 10 in one tree and you claim the barding, you can re-spec it but can not claim the barding of the second tree (Because you have claimed the barding from the NPC)

Getting your second set of Barding will be faster though, because once your chocobo caps you will receive 11 points and so on ^^