Will a PS3 save work with PS4?
Yes. If you get Destiny on a PS4, you will be able to play your character on both the PS3 and PS4. You won't be able to move from Playstation to Xbox, however.
Just like hopping worlds, you can use the same Guardian on Next Gen and Legacy Gen consoles – so long as you stay in the same system. Ergo, you can move from PlayStation to PlayStation and from Xbox to Xbox, but not across product lines.
From Bungie