I'm a rightly (& probably do to conditioning, also); here's my feelings:
Atari 2600: Love the stick right, button left thumb. I grew up on this. Only problem is there's only one button.
Arcade digital stick & 1 button: (Includes 2 buttons but only one is primary button) Usually ambi, and sometimes I swap in between levels just for the fun of it if buttons are mirrored on both sides of stick. Two exceptions:
Button(s) need rapid presses: I'm faster with my right, but I like to swap when my right gets tired. Once it's rested, I swap back to using my right for buttons.
Rotary stick: Right is much better at spinning the rotary, and feel more relaxed with right on rotary. Can survive with rotary on left side, though. My WIP two player rotary CP has 2 buttons on each side of both sticks.
Arcade digital & 2 buttons: Depends on game. Usually stick left, buttons right, but not always. Some games I can swap. And a couple I like buttons left, stick right for some reason. (Don't remember which ones ATM)
Arcade digital stick & three or more buttons: Standard stick left, buttons left.
Trackball: trackball right, buttons left, except when spinning the ball right or down-right. Left gets faster spin in those two directions. My one trackball test CP has buttons both sides; my two trackball CP has button to left of the TBs (couldn't fit on both sides).
Spinner: spiner right, buttons left. Planning to have buttons on both sides of the spinners on my two spinner CP.
Trigger/thumb stick: feels nicer with right, but I actually play better with my left if only a trigger button. If both trigger & thumb button, right wins both in feel and preformance. My 2 player thumb & trigger stick CP has buttons on both sides of both sitick.
Analog stick: Same as trigger stick.
Gamepads: dislike left thumb d-pad/stick, buttons right thumb, but can survive if there is one primary button. Once there is two primary buttons, or four or more total buttons, or trugger buttons, I suck with a gmaepad. In all cases, I always do better with full-size stick left & buttons right than any gamepad I have tried.
Mouse & keyboard: mouse right, keyboard left.