Uhm, I think you missed my point entirely. What brand a stick is or what genre of games it’s preferred for has nothing to do with it. The shoot 'em up fan’s typically preferred stick, the Seimitsu LS-32 still wouldn’t be suitable for the purpose of controlling a game with analog inputs because it’s a digital controller.
What I’m talking about is type of electronics:
With analog controls the precise attenuation of the input makes a difference in the electrical frequency, allowing you finite level of control pendent on how hard you push, where you position your controls, ect. ect. This is what allows you the various degrees of control needed to tiptoe past the Pirahna Plants or run circles 'round the eyeballs super fast in Super Mario 64 using the N64 joystick alone.
With digital controls you wouldn’t be able to do this. There’d be a button that either registers as either “on” or “off” so you’d only be able to move around at a pre-determined momentum, unless another button is pressed, more like Super Mario World. Electroncially speaking, most arcade joysticks operate like this.
I’m basically basically saying can’t properly play Mario 64 with an SNES game pad, even with a converter, no matter how good the latter might be for platformers. The mechanics of the game don’t match up with the physics of the controller and it breaks the game.
Try experimenting with your controller’s thumb-sticks in different positions if you haven’t already.