Momentary, in that the actual mute function is software-controlled. However, on the Amazon device it does trigger a physical power-down of the microphones, which is hardware-tied to the LED, so you can be sure that when the LED says the mics are off they really are off. I'm not sure about the Google one.

Edit: at least the physical slide switch on the Home Mini is a hardware cut-off; I assume the same is true of the Home Max.