I expect all of our characters will be stored server side linked to your XBL/PSN account, meaning any character you create on your Xbox 360 would show up on your new Xbox One. If characters were stored locally on the consoles...well...it just introduces many different kinds of issues that range from editing/copying saves to transfer issues.
Again, this is just my expectation.
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Local saves would pose a huge threat to the longevity of the game.
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Definitely. And you know that after enough time, someone would develop an application that allows us to add anything we want to saves if we had direct access; example: Gibbed for Borderlands 2.