there are several joysticks for the amiga that had two buttons (actual two button sticks not a one button stick with two buttons)
i had a friend who swore by joystick and i liked gamepads, so we had contests with several different game systems, and games him with the stick me with the pad and i beat him every time. he tried a gamepad for a while and got better.
joystick are made for flight sims and the like. they are ok for for driving sims.
one of the worst was superfrog, because it was such a great game. cool graphics, music and sound but up to jump was terrible. plus when you got the little ball thingie and wings the button would do different things at different times, with the same button. i dont remeber if it had a two button setting. ill go check