The Gottlieb stick's balltop is similar in size to the Nintendo sticks and Sega's Frogger stick but I'm pretty sure Gottlieb made their own controls. They were a fairly large company mainly focusing on pinball machines but they obviously had manufacturing plant and were fully capable of designing their own joysticks along with all the parts they made for their pinball machines. The Q-bert stick is a leafswitch based stick. I'm pretty sure Paige Oliver has an original Q-stick laying around so maybe he could post pics. I know I'd like to see a close up of the stick just to see what it looks like. I'm pretty sure that the square base of the stick gets mounted in the same position as a regular stick but I think the four leafswitches themselves are positioned diagonally which makes it a little different from a regular 4-way. Of course you can get the same effect by just turning a regular 4-way stick and mounting the whole base on a 45 degree angle. Maybe Paige can confirm the differences as I am not positive on this.
Thanks for the info. And it seems I'm not crazy, I always thought that I remember Frogger having a small red ball top. All the Frogger machines I see now just seem to have standard Wico 4 ways. I've been playing the game with my Pac Man joystick which seems to be OK.