I have two XLR cables going from the Axe-Fx III's Output 2 jacks (set to -10db) to a Matrix GT1000FX.
I play this rig at the house a lot and it's super easy to keep the volume anywhere between whisper quiet to "normal TV volume" using only the Axe-Fx's output knobs, even with the Matrix's volume knobs maxed. The Axe-Fx allows for extremely fine output level control at low volumes.
I was actually not expecting the Axe + dimed Matrix combo to be as good as it is at low volume control, but it's fine. The volume never leaps up if you breathe on it funny, like what happens with some tube amps, or anything like that.
Also, with a single 16 ohm 4x12 cab, if you just use one channel of the Matrix (meaning if you keep it in Stereo mode and not in Bridged mode), it will only push 150 watts to the cab at max. So if you keep your output levels on the Axe-Fx low, you'll never even come close to that. For reference, at TV volumes, you're probably actually only sending somehwere between 0.05 and 0.25 watts to the cab or something crazy low like that.