Southpaw (I'm right-handed tho) + inverted X\Y-axes in FPS, inverted Y-axis in TPS. Used to play like this since GE007 on N64.
But here's a problem, modern FPSs use face buttons in action, so I need to stop moving->peform action (jump for example)->put my thumb on right stick again to move further - this's rather disturbing. Sometimes I need to move right stick and press face button simultaneously, which is very uncomfortable. The better way to resolve this situation is to map those action buttons on d-pad instead of face buttons (for southpaw configuration), but in most FPSs there're no option like this.
P.S.: I wonder, why there still no trackball instead of this stupid right stick on modern gamepads? Little effort - great increase in accuracy in console shooters, almost like mouse, no need in motion controls.