I am playing a US version of Pokémon X or Pokémon Y on a US-version Nintendo 3DS and a Japanese version of Pokémon X or Pokémon Y on a Japanese Nintendo 3DS. If I want to put all of the Pokémon I've collected in these games in one Pokémon Bank, can I download Pokémon Bank on either my Japanese or my US Nintendo 3DS system and insert the Game Cards for the different regions in it? Will Pokémon Bank and Poké Transporter be limited by regional restrictions?
APokémon X and Pokémon Y have regional restrictions and cannot be played on a system from the Nintendo 3DS family that is not from the same region as the Game Card. However, Pokémon Bank and Poké Transporter are made to work with all regional versions of Pokémon X and Pokémon Y, so you can insert Pokémon X or Pokémon Y games from any region into the Nintendo 3DS system that you have downloaded Pokémon Bank into, and deposit and withdraw your Pokémon as you like.
However, please note that Nintendo makes no guarantee for the performance of software or systems in the Nintendo 3DS family when used outside their intended regions. If any trouble should occur when using software or systems outside their intended regions, you will not be able to receive any support beyond the country where the software or systems were made to be sold.