I think of Fallout 3 as more of an RPG than a shooter, but then again, i almost exclusively use VATS to shoot.
But that may actually be the point; how much can one deviate from the 'default' FPS mechanics and still be rightfully called an FPS? The 'genre defaults', for lack of a better word, almost forces the games to be very much alike. Or they wouldn't be called an FPS.
For instance, I think Left 4 Dead (only played the demo though) is very different from, say, CoD 4 or Halo. But in my mind Left is more of a modern version of Gauntlet than 'an FPS'. It just happens to have a first-person view.
Mirror's Edge? No shooting (or just very little), hence not an FPS.
Bioshock felt different, but that's mostly the art deco surroundings, and not the gameplay. GoW actually did feel different for me, with the focus on finding cover instead of shooting first.
So i agree with an earlier poster in this thread; try mixing genres if you feel this way. Maybe you'll find something you like. I had a similar feeling a few years ago when I almost exclusively played (J)RPGs, and getting something totally different from my usual games choice really got me going again.