@Ivotas:
I think that dawn and new dawn are exactly the same because every upcoming dawn is a new dawn just like every day is a new day compared to what came before. And from the way how this entire story about the OP worlds history is presented it seems to be a several centuries long wait for the dawn to finally arrive.
Don't forget that Pedro said that Luffy and his crew are the ones who will guide the minks and the kozuki family to the dawn of the world. So one can read from Pedro's words that neither one of the minks nor one of the kozuki will guide them to the dawn of the world. So I think that momo, who will guide the world to the dawn, doesn't have the same dawn meaning as Luffy. So it makes no sense that Momo and Luffy have the same role with the dawn because Momo from the kozuki family is someone who does not guide the minks and the kozuki to the dawn of the world.
According to what Pedro said, the dawn of the world is about guiding the world to a new dawn. That's why I think Luffy guides the world to a new dawn after Momo guides the world to the dawn.