Just announced at https://www.facebook.com/FinalFantasyXIV:

FINAL FANTASY XIV: A Realm Reborn PlayStation 3 users will be able to upgrade to the PS4 version for free!

Also, PS4 users will be able try out the Beta Test when it launches on Feb. 22, 2014! Stay tuned for more info in the future!

This is awesome and a great move on their part!