Benefits of multi-methods

I've mostly used and played around with C++, Ruby and Python which have no support for multi-methods. Now that OpenDylan is available, I can use it in a language which I admire. Here's how you can respond to an event in Dylan:

define method handle-event( event :: <button-down>, button == $left ) => ()
  [...]
end method;

define method handle-event( event :: <button-down>, button == $right ) =>()
  [...]
end method;

And here's the equivalent in pseudo-Java:

void handle_event( Event event, int button ) {
  if( event.isInstanceOf( ButtonDown ) ) {
    if( button == LEFT_BUTTON ) {
      [...]
    } else if( button == RIGHT_BUTTON ) {
      [...]
    }
  }
}

That is an entangled mess of spaghetti.