Wireless is the way to go.
When the PlayStation 4 launched late last year, Sony made the new Dual Shock 4 controller compatible with the PS3 if it was plugged in via USB cable. However, that meant players were limited to the very short charge cable.
Now, thanks to recent firmware update 4.60, the PS4 controller can be used wirelessly with the PS3. If you want to know how it works, check out the detailed information at Reddit . Basically, you just pair the PS4 controller with the PS3 by using the system's Bluetooth capabilities, which is relatively simple. The only downside is that many of the Dual Shock 4's features, including the PlayStation button, vibration and Sixaxis tilt controls don't work.
At the very least, though, you can turn on the PS3 using the Dual Shock 4's PS button, which you couldn't do before. So, plan on using the newer controller to play older games?