I played both for a few days and for whatever reason decided P3D was for me... maybe it was the familiar feeling of it being based off FSX and as a kid playing that game a ton.
Having 10 or so hours in the Redbird I would say that is very much so a flight simulator. You have realistic controls with working knobs and yoke resistance. Flight dynamics are still that of P3D which anyone who plays that (or Xplane or FSX) and flies real planes knows they are worlds apart.
Being that I do use my setup to 'train' on, I read a lot of the Flight Sim boards and most users seem to be very touching, referring to themselves as Hobbyists over Gamers and if you call it a game they get up in arms about that. I think it has to do with people wanting to take themselves more serious than they are.
Maybe it has more to do with how people are using it. For example mine is a flight simulator when I plan and fly an IFR flight in Heavy IMC, practicing comms, navigation and doing all the knob twisting and GPS setups and chart using.... but it's a game when I load up the Piper Cub and do touch and goes on the aircraft carrier in San Diego's bay.