You can use both switches, the difference is that the one with 3 pins has one common input and two outputs, one that is normally closed and the other that is normally opened.
In the first figure you can see a 2 pin switch and on the rightmost a 3 pin switch.
Then you connect the switch to the RJ45 (J1 element on the schematic) connector that will go to the vex joystick.
Also you can check the way Soapy29 made his competition control on this post