While not a pure flight sim, we are getting War Thunder if you will be upgrding to a PS4. Here is a video of a guy playing War Thunder with the OR; truly amazing in my opinion. Off topic but I truly hope that the PS4 will support the OR.
War Thunder the absolute closest you can get to a flight simulator using a Playstation controller. If you set the controls for realistic flight, the left stick controls the ailerons (roll) and elevators (pitch) and the right stick controls the rudder (yaw) and engine power (airspeed).
Flaps, landing gear and air brake are mapped to the d-pad.
I mentioned 'realistic' flight, and I really meant it. If you screw up with the controls, you can stall your plane and send it into an uncontrolled flatspin. If you bank too hard, you can 'blackout' from the g-forces (the screen actually starts to fade to gray/black).
Really, truly amazing game. Lots of tutorials to get you started, and you can even choose a 'test flight' mode for many of the aircraft that allows you to fly freely in a non-combat situation. Can't wait until this game goes live on this side of the pond so I can think about supporting the development of it with my own cash (the game is free-to-play, but will be supported with optional microtransactions).