If you choose to be reborn, you will not have magic powers, but you will unlock a status window and a skill tree that you can use to give yourself new skills and abilities and improve your physical characteristics.
You’ll get the same thing if you choose to be reincarnated, however, magic will be a factor. And the age of the world will be somewhere like 50-ish years before the full rollout of the industrial revolution, technology-wise. (minor clarification, you keep your current knowledge either way)
However, you will not be the hero or the chosen one. You’re just going to be a person with a perk.
No, it’s New Game+. You would start over back on the day that you were born.
Your superpower in this case would be your ability to remember events that have happened over the course of your life and potentially profit from them or to change their outcome, that and the status board and its ability to upgrade yourself or to give yourself perks in the process over the course of your life.