TL;DR: Momentary switches are compatible with the Champion board's logic, latching switches are not.
Latching switches are switches that "latch" into the on position when pressed, then "latch" off when pressed again. They are best used in a stunt hilt where you need to cut off current flow entirely when off.
Momentary switches don't latch, so they only allow current when they are pressed. This wouldn't work well for a stunt saber unless you want to keep your hand on the button the whole time you use it, but it's perfect for sending burst signals to the logic of your soundboard (Champion and Hero). The board registers a button press whenever the switch goes from a "low" state to a "high" state, and can identify a held button by the amount of time it remains in that "high" state. If you were to use a latching switch for that you would need to press the button twice (on and off) in rapid succession to send a "press" signal, adding a delay between presses to send a "hold" signal. For that reason, the momentary switch is the only type that will work properly with the Champion boards.
Getting a bit more in depth, some advanced boards that require multiple switches allow you to use either a latching or momentary switch for the main switch, but require a momentary switch for the aux switch. Changes can be made to the logic to see "press" commands from a latching switch, however those same changes prevent it from seeing "hold" signals. In these boards it just so happens that all of the "hold" options are on the Aux switch, so they can allow latching switches as the main (though it's still generally recommended to use a momentary anyways).