If you log into D1 on your XBox One with the same XBox account you played with on the XBox 360 then it should give you the option to migrate your D1 progress from the X360 to the D1 XBox One version of the game.
If in the past you ever logged into D1 on an XBox One then the one migration acceptance or rejection you get would have already been used.
Once you convert to the D1 XBox One version your D1 game progress will be irrevocably split between XBox 360 and XBox One. If you never plan on going back to D1 on the XBox 360 then it won't matter. But if you plan on jumping between playing D1 on Xbox 360 and XBox One then progress after the split will not be shared between the two platforms.