Cost will depend on when you do it. As I recall from the migration from PS3 to PS4, Square was offering to let people move between the platforms for free when the PS4 first came out. I didn't do it at the time because I hadn't bought the new system (no games I wanted yet, so I didn't want to spend the money on it) and by the time I did upgrade my system, that was no longer an option, and I had to purchase the game again.