The GameCube's Resident Evil remake is getting the HD treatment on Windows, Sony, and Microsoft machines, but only over PlayStation Network will the game be a cross-buy title. For $19.99, you'll be able to purchase either the PS3 or PS4 version and get the other without paying an extra cent.
Unfortunately, it sounds like cross-buy will only be available to pre-order customers. You will get a free theme, however, and the game will be pre-loaded so that you can start playing at midnight on launch day.
Resident Evil will hit PS4 and PS3 (as well as Windows, Xbox One, and Xbox 360) on January 20, 2015.