Unfortunately, your collection of DualShock 3 controllers won't work with PS4. However, you shouldn't feel too bad about throwing them away--especially as you'll be able to use your DualShock 4 on your PS3.
A new video by Udetto (via All Games Beta) shows off Sony's next-gen controller connected to a PS3. It appears all the inputs work as expected. However, there is a caveat: you won't be able to use the DualShock 4 wirelessly. In addition, it appears there's no "PS Button" function, as the touch pad serves as the Start button.
The video doesn't detail whether or not rumble works, and doesn't go into detail on compatibility issues faced while playing FIFA 14. Still, with DualShock 4 working on PS4 (somewhat), PC, Vita TV, and now, PS3, it seems like a rather handy controller to have--especially if you plan on gaming across multiple devices.