Noein: Mou Hitori no Kimi e, Asura Cryin' Recommendations
Both shows depict 'the end of the world' if something is not done and a tool can be used to create the 'perfect' world.
Noein focuses more on dragon knights trying to protect their timeline called La'cryma from Shangri-la's invasion. The knights require an 'object' called 'Dragon Torque'. As they accidentally stumble into the present, they realise that this timeline is very similar to theirs. One of the knights chose to protect her while others insists that the dragon torque is just an illusion to them. As time goes by, they let the Dragon Torque choose for herself, to create a world that is