This comes down to a style thing really. Both will perform exactly the same way in code.
The separate class will tend to keep the code inside your actual method simpler, whereas the anonymous inner class brings the code for the listener implementation within the method which can make it clearer what it is doing.
There is also the case that anonymous inner classes can access final variables in the method that creates them. You can't do that with a pre-written class (although you can pass the variables into the controller).
The separate code is re-usable - so if you have the same listener in multiple places then it is the clear winner.